For I know that Kelvin is always positive, but why in the example, why Kevin degree is negative?

Couple things: 1. Be careful not to call it "Kelvin degree" or "degrees Kelvin." They are called "kelvins" (lowercase K). 2. The temperature in kelvins is still positive, but the CHANGE was negative.

i did not understand how chemists use the melting point to identify the purity of a substance

Chemists can heat up substances to the point when they start to melt. At this temperature, the chemists can compare this value to a table of standard results from a data table/source/reference. The standard results are the true results for that particular substance. However, when a substance has an experimental melting point significantly higher than the standard data book value, then we know there must be impurities present. Impurities may have a higher melting point than the substance we're interested in, so the overall melting point for the impure substance is higher than expected.

Why the Zeroth Law of thermodynamics is called so,is it the most basic law?

zeroth law was discovered after the first law and other thermodynamic laws and because it was the most basic law they named it zeroth law.

Underneath the picture of the ice cubes, the caption reads, "As ice melts, heat is transferred from the water to the surroundings." Shouldn't it read, "As ice melts, heat is transferred from the surroundings to the ice" or something similar?

yeah, i would say you're right. heat is always spontaneously transferred from (object of) higher to lower temperature.

Why is it in my book it is indicated that q = C x change in T, where C is heat capacity (J/C). C is then equal to (m x s x change in T)hot + (m x s x change in T)cold/-change in T, where s is the specific heat capacity (J/gC). Can you please explain to me? I'm quite confused.

q = CΔT and q = msΔT, so C = ms. C is the *total* heat capacity of the object. s is the *specific* heat capacity, i.e. the heat capacity per gram. If you multiply the heat capacity per gram (s) by the number of grams, you get the total heat capacity (C). Usually you know the specific heat capacity for water, but you don't know the specific heat capacity of the calorimeter. But it is quite easy to do a separate experiment to determine the total heat capacity of the calorimeter. You often set up your calculations like this: heat for water + heat for object + heat for calorimeter = 0 q₁ + q₂ + q₃ = 0. q₁ = m₁s₁ΔT₁ for the water q₂ = m₂s₂ΔT₂ for the object q₃ = CΔT for the calorimeter. If you then know everything but one of the variables, you can calculate it from the above equations .

Why do kelvins don't have degree?

In general, 'degrees' are found in units which are mainly arbitrary. Fahrenheit and Celsius are meant to be convenient instead of absolute. The same goes for angle degrees, since that also divides the circle into 360 degrees arbitrarily. Like, there is no 'degrees' in radians, which is the 'natural' way of measuring angles. The kelvin is the SI base unit of temperature. it is the absolute temperature scale. *By absolute we mean that the zero on the Kelvin scale, denoted by 0 K, is the lowest temperature that can be attained theoretically*. On the other hand, 0 F and 0 C are based on the behavior of an arbitrarily chosen substance. For Kelvin. Temperature is defined in terms of the average energy of particles in a system, and Kelvin is directly proportional to that -- the zero in the Kelvin scale corresponds to absolute zero, and not any arbitrary temperature, and Kelvin is the 'natural' unit to measure temperature.

Difference between work and heat?

Work is a measure of amount of energy transferred to the system by applying force on it along the displacement , heat is the process of transferring of energy between two systems due to difference in the temperature

Can somebody give me an example that shows the difference between heat and temperature?

A thermometer shows the temperature because it measures (compare) the degree of agitation of its molecules in relation to the degree of agitation of the molecules of the environment, but this is only possible because you transfer heat to the thermometer. This is because 2 bodys at different temperatures tend to get in the thermal balance between them with the one that is hot by giving energy to the coldest in the form of heat, so on a cold day you wear a jacket not to heat yourself but to reduce the loss of thermal energy to the environment in the form of heat.

Why is the heat of an iceberg greater than that of a pot of boiling water?

Heat isn’t something that objects possess. Thermal energy, the energy associated with an object’s temperature, is what people usually mean when they say heat. Heat itself is the transfer of thermal energy from one object to another. Thermal energy is the thing that object possess, but heat is a process that occurs between objects. If we compare an iceberg to a pot of boiling water, each of the molecules of both objects have their own amount of thermal energy. All pieces of matter, even very cold ones, have at least some thermal energy because they are in motion at the atomic scale and this is motion is thermal energy. Probably the part that confuses people with a question like this is that a pot of boiling water is hotter than an iceberg and we associated high temperature with thermal energy. Which that is partially true, but temperature is a measure of the average thermal energy of all molecules in a system. The pot’s molecules are on average more energetic than the iceberg’s molecules, but the iceberg has substantially more molecules than the pot. And the total amount of all these iceberg molecule’s thermal energies is greater than the pot’s molecule’s total thermal energy. Hope that helps.

Main content

Course: Chemistry library > Unit 13

Lesson 1: Internal energy

Heat and temperature

Google Classroom

What heat means in thermodynamics, and how we can calculate heat using the heat capacity.

Key points

Heat, $q$ ‍, is thermal energy transferred from a hotter system to a cooler system that are in contact.
Temperature is a measure of the average kinetic energy of the atoms or molecules in the system.
The zeroth law of thermodynamics says that no heat is transferred between two objects in thermal equilibrium; therefore, they are the same temperature.
We can calculate the heat released or absorbed using the specific heat capacity $C$ ‍, the mass of the substance $m$ ‍, and the change in temperature $Δ T$ ‍ in the equation:

$q = m \times C \times Δ T$ ‍

Heat in thermodynamics

What contains more heat, a cup of coffee or a glass of iced tea? In chemistry class, that would be a trick question (sorry!). In thermodynamics, heat has a very specific meaning that is different from how we might use the word in everyday speech. Scientists define heat as thermal energy transferred between two systems at different temperatures that come in contact. Heat is written with the symbol q or Q, and it has units of Joules (

J

Heat is sometimes called a process quantity, because it is defined in the context of a process by which energy can be transferred. We don't talk about a cup of coffee containing heat, but we can talk about the heat transferred from the cup of hot coffee to your hand. Heat is also an extensive property, so the change in temperature resulting from heat transferred to a system depends on how many molecules are in the system.

Relationship between heat and temperature

Heat and temperature are two different but closely related concepts. Note that they have different units: temperature typically has units of degrees Celsius (

^{\circ} C

) or Kelvin (

K

), and heat has units of energy, Joules (

J

). Temperature is a measure of the average kinetic energy of the atoms or molecules in the system. The water molecules in a cup of hot coffee have a higher average kinetic energy than the water molecules in a cup of iced tea, which also means they are moving at a higher velocity. Temperature is also an intensive property, which means that the temperature doesn't change no matter how much of a substance you have (as long as it is all at the same temperature!). This is why chemists can use the melting point to help identify a pure substance

-

the temperature at which it melts is a property of the substance with no dependence on the mass of a sample.

On an atomic level, the molecules in each object are constantly in motion and colliding with each other. Every time molecules collide, kinetic energy can be transferred. When the two systems are in contact, heat will be transferred through molecular collisions from the hotter system to the cooler system. The thermal energy will flow in that direction until the two objects are at the same temperature. When the two systems in contact are at the same temperature, we say they are in thermal equilibrium.

Zeroth law of thermodynamics: Defining thermal equilibrium

The zeroth law of thermodynamics defines thermal equilibrium within an isolated system. The zeroth law says when two objects at thermal equilibrium are in contact, there is no net heat transfer between the objects; therefore, they are the same temperature. Another way to state the zeroth law is to say that if two objects are both separately in thermal equilibrium with a third object, then they are in thermal equilibrium with each other.

The zeroth law allows us to measure the temperature of objects. Any time we use a thermometer, we are using the zeroth law of thermodynamics. Let's say we are measuring the temperature of a water bath. In order to make sure the reading is accurate, we usually want to wait for the temperature reading to stay constant. We are waiting for the thermometer and the water to reach thermal equilibrium! At thermal equilibrium, the temperature of the thermometer bulb and the water bath will be the same, and there should be no net heat transfer from one object to the other (assuming no other loss of heat to the surroundings).

Heat capacity: Converting between heat and change in temperature

How can we measure heat? Here are some things we know about heat so far:

When a system absorbs or loses heat, the average kinetic energy of the molecules will change. Thus, heat transfer results in a change in the system's temperature as long as the system is not undergoing a phase change.
The change in temperature resulting from heat transferred to or from a system depends on how many molecules are in the system.

We can use a thermometer to measure the change in a system's temperature. How can we use the change in temperature to calculate the heat transferred?

In order to figure out how the heat transferred to a system will change the temperature of the system, we need to know at least

2

things:

The number of molecules in the system
The heat capacity of the system

The heat capacity tells us how much energy is needed to change the temperature of a given substance assuming that no phase changes are occurring. There are two main ways that heat capacity is reported. The specific heat capacity (also called specific heat), represented by the symbol

c

C

, is how much energy is needed to increase the temperature of one gram of a substance by

1^{\circ} C

1 K

. Specific heat capacity usually has units of

\frac{J}{grams \cdot K}

. The molar heat capacity,

C_{m}

C_{mol}

, measures the amount of thermal energy it takes to raise the temperature of one mole of a substance by

1^{\circ} C

1 K

, and it usually has units of

\frac{J}{mol \cdot K}

. For example, the heat capacity of lead might be given as the specific heat capacity,

0.129 \frac{J}{g \cdot K}

, or the molar heat capacity,

26.65 \frac{J}{mol \cdot K}

Let's think about what is happening on a molecular level when we add thermal energy to some molecules. The thermal energy can be stored as vibrations and rotations between atoms within a molecule, which does not significantly increase the temperature of the system. The energy can also be used to disrupt intermolecular interactions and increase the velocity of the entire molecule, which increases the translational kinetic energy of the molecule.

Temperature is primarily a measure of the translational kinetic energy of the system. Depending on the molecular structure and intermolecular interactions, different substances can store different amounts of thermal energy as vibrations and rotations before the temperature increases.

Calculating $q$ ‍ using the heat capacity

We can use the heat capacity to determine the heat released or absorbed by a material using the following formula:

$q = m \times C \times Δ T$ ‍

where

m

is the mass of the substance (in grams),

C

is the specific heat capacity, and

Δ T

is the change in temperature during the heat transfer. Note that both mass and specific heat capacity can only have positive values, so the sign of

q

will depend on the sign of

Δ T

. We can calculate

Δ T

using the following equation:

$Δ T = T_{final} - T_{initial}$ ‍

where

T_{final}

and

T_{initial}

can have units of either

^{\circ} C

K

. Based on this equation, if

q

is positive (energy of the system increases), then our system increases in temperature and

T_{final} > T_{initial}

. If

q

is negative (energy of the system decreases), then our system's temperature decreases and

T_{final} < T_{initial}

Example problem: Cooling a cup of tea

Let's say that we have

250 mL

of hot tea which we would like to cool down before we try to drink it. The tea is currently at

370 K

, and we'd like to cool it down to

350 K

. How much thermal energy has to be transferred from the tea to the surroundings to cool the tea?

We are going to assume that the tea is mostly water, so we can use the density and heat capacity of water in our calculations. The specific heat capacity of water is

4.18 \frac{J}{g \cdot K}

, and the density of water is

1.00 \frac{g}{mL}

. We can calculate the energy transferred in the process of cooling the tea using the following steps:

1. Calculate the mass of the substance

We can calculate the mass of the tea/water using the volume and density of water:

$m = 250 mL \times 1.00 \frac{g}{mL} = 250 g$ ‍

2. Calculate the change in temperature, $Δ T$ ‍

We can calculate the change in temperature,

Δ T

, from the initial and final temperatures:

$\begin{aligned} Δ T & = T_{final} - T_{initial} \\ = 350 K - 370 K \\ = - 20 K \end{aligned}$ ‍

Since the temperature of the tea is decreasing and

Δ T

is negative, we would expect

q

to also be negative since our system is losing thermal energy.

3. Solve for $q$ ‍

Now we can solve for the heat transferred from the hot tea using the equation for heat:

$\begin{aligned} q & = m \times C \times Δ T \\ = 250 g \times 4.18 \frac{J}{g \cdot K} \times - 20 K \\ = - 21000 J \end{aligned}$ ‍

Thus, we calculated that the tea will transfer

21000 J

of energy to the surroundings when it cools down from

370 K

350 K

Conclusions

In thermodynamics, heat and temperature are closely related concepts with precise definitions.

Heat, $q$ ‍, is thermal energy transferred from a hotter system to a cooler system that are in contact.
Temperature is a measure of the average kinetic energy of the atoms or molecules in the system.
The zeroth law of thermodynamics says that no heat is transferred between two objects in thermal equilibrium; therefore, they are the same temperature.
We can calculate the heat released or absorbed using the specific heat capacity $C$ ‍, the mass of the substance $m$ ‍, and the change in temperature $Δ T$ ‍ in the following equation:

$q = m \times C \times Δ T$ ‍

Attributions

This article was adapted from the following articles:

“Introduction to Thermodynamics” from Boundless Chemistry, CC BY-SA 4.0.
"The Zeroth Law of Thermodynamics" from Boundless Physics, CC BY-SA 4.0.
"Heat Capacity" from UC Davis ChemWIki, CC BY-NC-SA 3.0 US.

The modified article is licensed under a CC-BY-NC-SA 4.0 license.

Additional References

Kotz, J. C., Treichel, P. M., Townsend, J. R., and Treichel, D. A. (2015). Specific Heat Capacity: Heating and Cooling. In Chemistry and Chemical Reactivity, Instructor's Edition (9th ed., pp. 184-189). Stamford, CT: Cengage Learning.

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Tu Huynh
Posted 8 years ago. Direct link to Tu Huynh's post “For I know that Kelvin is...”
For I know that Kelvin is always positive, but why in the example, why Kevin degree is negative?
Button navigates to signup pageComment on Tu Huynh's post “For I know that Kelvin is...”
(6 votes)
Answer
- C Hart
  Posted 8 years ago. Direct link to C Hart's post “Couple things: 1. Be car...”
  Couple things:
  1. Be careful not to call it "Kelvin degree" or "degrees Kelvin." They are called "kelvins" (lowercase K).
  2. The temperature in kelvins is still positive, but the CHANGE was negative.
  Comment on C Hart's post “Couple things: 1. Be car...”
  (50 votes)
Nanananananananana
Posted 8 years ago. Direct link to Nanananananananana's post “Why is it in my book it i...”
Why is it in my book it is indicated that q = C x change in T, where C is heat capacity (J/C). C is then equal to (m x s x change in T)hot + (m x s x change in T)cold/-change in T, where s is the specific heat capacity (J/gC). Can you please explain to me? I'm quite confused.
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Ernest Zinck
  Posted 8 years ago. Direct link to Ernest Zinck's post “q = CΔT and q = msΔT, so ...”
  q = CΔT and q = msΔT, so C = ms.
  C is the total heat capacity of the object.
  s is the specific heat capacity, i.e. the heat capacity per gram.
  If you multiply the heat capacity per gram (s) by the number of grams, you get the total heat capacity (C).
  Usually you know the specific heat capacity for water, but you don't know the specific heat capacity of the calorimeter.
  But it is quite easy to do a separate experiment to determine the total heat capacity of the calorimeter.
  
  You often set up your calculations like this:
  heat for water + heat for object + heat for calorimeter = 0
  q₁ + q₂ + q₃ = 0.
  q₁ = m₁s₁ΔT₁ for the water
  q₂ = m₂s₂ΔT₂ for the object
  q₃ = CΔT for the calorimeter.
  If you then know everything but one of the variables, you can calculate it from the above equations .
  Comment on Ernest Zinck's post “q = CΔT and q = msΔT, so ...”
  (17 votes)
danishsa314
Posted 8 years ago. Direct link to danishsa314's post “i did not understand how ...”
i did not understand how chemists use the melting point to identify the purity of a substance
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Rohan Bassi
  Posted 8 years ago. Direct link to Rohan Bassi's post “Chemists can heat up subs...”
  Chemists can heat up substances to the point when they start to melt. At this temperature, the chemists can compare this value to a table of standard results from a data table/source/reference. The standard results are the true results for that particular substance. However, when a substance has an experimental melting point significantly higher than the standard data book value, then we know there must be impurities present. Impurities may have a higher melting point than the substance we're interested in, so the overall melting point for the impure substance is higher than expected.
  Comment on Rohan Bassi's post “Chemists can heat up subs...”
  (11 votes)
Fatima Naz
Posted 7 years ago. Direct link to Fatima Naz's post “Why do kelvins don't have...”
Why do kelvins don't have degree?
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(3 votes)
Answer
- Abdülrezzak Bostani
  Posted 7 years ago. Direct link to Abdülrezzak Bostani's post “In general, 'degrees' are...”
  In general, 'degrees' are found in units which are mainly arbitrary. Fahrenheit and Celsius are meant to be convenient instead of absolute. The same goes for angle degrees, since that also divides the circle into 360 degrees arbitrarily. Like, there is no 'degrees' in radians, which is the 'natural' way of measuring angles.
  
  The kelvin is the SI base unit of temperature. it is the absolute temperature scale. By absolute we mean that the zero on the Kelvin scale, denoted by 0 K, is the lowest temperature that can be attained theoretically. On the other hand, 0 F and 0 C are based on the behavior of an arbitrarily chosen substance.
  
  For Kelvin. Temperature is defined in terms of the average energy of particles in a system, and Kelvin is directly proportional to that -- the zero in the Kelvin scale corresponds to absolute zero, and not any arbitrary temperature, and Kelvin is the 'natural' unit to measure temperature.
  Comment on Abdülrezzak Bostani's post “In general, 'degrees' are...”
  (13 votes)
Suraj Singh
Posted 8 years ago. Direct link to Suraj Singh's post “Why the Zeroth Law of the...”
Why the Zeroth Law of thermodynamics is called so,is it the most basic law?
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(5 votes)
Answer
- Mohd. Nomaan
  Posted 8 years ago. Direct link to Mohd. Nomaan's post “zeroth law was discovered...”
  zeroth law was discovered after the first law and other thermodynamic laws
  and because it was the most basic law they named it zeroth law.
  Comment on Mohd. Nomaan's post “zeroth law was discovered...”
  (9 votes)
aricohens13
Posted 7 years ago. Direct link to aricohens13's post “Underneath the picture of...”
Underneath the picture of the ice cubes, the caption reads, "As ice melts, heat is transferred from the water to the surroundings." Shouldn't it read, "As ice melts, heat is transferred from the surroundings to the ice" or something similar?
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Answer
- skofljica
  Posted 7 years ago. Direct link to skofljica's post “yeah, i would say you're ...”
  yeah, i would say you're right. heat is always spontaneously transferred from (object of) higher to lower temperature.
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Kay Johnson
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Why is it often not possible to directly measure the heat energy change of the reactants and products?
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- jd.agg6961
  Posted 6 years ago. Direct link to jd.agg6961's post “Can two bodies of differe...”
  Can two bodies of different temperatures in thermal contact do not necessarily attain a mean temperature. Explain the reason behind this
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ac4444122
Posted 6 years ago. Direct link to ac4444122's post “Can somebody give me an e...”
Can somebody give me an example that shows the difference between heat and temperature?
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- Lucas De Oliveira
  Posted 6 years ago. Direct link to Lucas De Oliveira's post “A thermometer shows the t...”
  A thermometer shows the temperature because it measures (compare) the degree of agitation of its molecules in relation to the degree of agitation of the molecules of the environment, but this is only possible because you transfer heat to the thermometer. This is because 2 bodys at different temperatures tend to get in the thermal balance between them with the one that is hot by giving energy to the coldest in the form of heat, so on a cold day you wear a jacket not to heat yourself but to reduce the loss of thermal energy to the environment in the form of heat.
  Button navigates to signup page
  (4 votes)
Keitumetse Madiga
Posted a year ago. Direct link to Keitumetse Madiga's post “Why is the heat of an ice...”
Why is the heat of an iceberg greater than that of a pot of boiling water?
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(0 votes)
Answer
- Richard
  Posted a year ago. Direct link to Richard's post “Heat isn’t something that...”
  Heat isn’t something that objects possess. Thermal energy, the energy associated with an object’s temperature, is what people usually mean when they say heat. Heat itself is the transfer of thermal energy from one object to another. Thermal energy is the thing that object possess, but heat is a process that occurs between objects.
  
  If we compare an iceberg to a pot of boiling water, each of the molecules of both objects have their own amount of thermal energy. All pieces of matter, even very cold ones, have at least some thermal energy because they are in motion at the atomic scale and this is motion is thermal energy. Probably the part that confuses people with a question like this is that a pot of boiling water is hotter than an iceberg and we associated high temperature with thermal energy. Which that is partially true, but temperature is a measure of the average thermal energy of all molecules in a system. The pot’s molecules are on average more energetic than the iceberg’s molecules, but the iceberg has substantially more molecules than the pot. And the total amount of all these iceberg molecule’s thermal energies is greater than the pot’s molecule’s total thermal energy.
  
  Hope that helps.
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Ayudh Saxena
Posted 8 years ago. Direct link to Ayudh Saxena's post “Difference between work a...”
Difference between work and heat?
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- Mohamed Ossama
  Posted 8 years ago. Direct link to Mohamed Ossama's post “Work is a measure of amou...”
  Work is a measure of amount of energy transferred to the system by applying force on it along the displacement , heat is the process of transferring of energy between two systems due to difference in the temperature
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Chemistry library

Course: Chemistry library > Unit 13

Key points

Heat in thermodynamics

Relationship between heat and temperature

Zeroth law of thermodynamics: Defining thermal equilibrium

Heat capacity: Converting between heat and change in temperature

Calculating q‍ using the heat capacity

Example problem: Cooling a cup of tea

1. Calculate the mass of the substance

2. Calculate the change in temperature, ΔT‍

3. Solve for q‍

Conclusions

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Calculating $q$ ‍ using the heat capacity

2. Calculate the change in temperature, $Δ T$ ‍

3. Solve for $q$ ‍