Topic 2

Question 1

What is heat capacity?

Answer 1

The heat capacity of a system is the amount of heat that must be supplied to raise its temperature by 1 K.

Heat supplied is path dependent because the heat supplied is not a function of state.

Question 2

Derive the heat capacity equation

Answer 2

𝐶_𝑝−𝐶_𝑉=𝑛𝑅= 𝑁𝑘_B

Question 3

What is the principle of equipartition of energy?

Answer 3

Each independent degree of freedom (quadratic energy term) contributes an amount 1/2 𝑘_𝐵 𝑇 to the total thermal energy.

(thermal energy is
shared equally by each independent energy storage term.)

Question 4

What is the total thermal energy of a monoatomic ideal gas?

Answer 4

3/2 𝑘_𝐵 𝑇=3/2nRT

Question 5

What is the heat capacity of a monatomic ideal gas ?

Answer 5

𝐶_𝑝=𝐶_𝑉 +nR = 5/2nR

𝐶_𝑉=3/2nR

Question 6

What is the heat capacity of a diatomic ideal gas ?

Answer 6

𝐶_𝑝=𝐶_𝑉 +nR = 7/2nR

𝐶_𝑉=5/2nR( for moderate temp)( for high its 7/2)

Question 7

How many degrees of freedom does a diatomic ideal gas have and what are they?

Answer 7

Diatomic gases have
3 translational degrees of freedom (translational kinetic energy in each x,
y and z),
2 rotational degrees of freedom (rotational kinetic energy term)
and 1 vibrational degree of freedom (vibrational kinetic
energy ). Vibrational degrees of freedom are often
‘frozen out’ apart from at very high temperatures.

Question 8

Why doesn’t the rotation around the x axis not contribute for rotational kinetic energy?

Answer 8

Rotation around the x axis does not contribute because we assume that the atoms are effectively point particles.

Question 9

What is the heat capacity of a solid?

Answer 9

𝐶_𝑉 =3R

Question 10

How many degrees of freedom does a solid have?

Answer 10

Each atom has 3 translational and 3

vibrational degrees of freedom

Question 11

What is a heat engine?

Answer 11

A heat engine is any device that transforms heat partly into work or mechanical energy

Question 12

What are reversible processes?

Answer 12

A process is carried out very slowly, so that the gas remains in equilibrium at all times.

Question 13

What are irreversible processes?

Answer 13

Processes that involve rapid change.

Question 14

How do you change the state of a gas?

Answer 14

Using different paths: adabatic, isobaric,isochoric and isothermal

Question 15

What is a isothermal process?

Answer 15

Isothermal processes occur at constant temperature. This follows a curve on a pV diagram

Question 16

What is a isobaric process?

Answer 16

Isobaric processes occur at constant pressure. This follows a horizontal line in a pV diagram

Question 17

What is a isochoric process?

Answer 17

Isochric processes occur at constant volume so there is no work
done, ∆W = 0. This follows a vertical line on a pV diagram

Question 18

What is a adiabatic process?

Answer 18

Adiabatic processes occur without transfer of heat i.e. ∆Q = 0

NO HEAT IN OR OUT

Question 19

What is the thermal efficiency of a heat engine?

Answer 19

η =W/QH= 1 −|QC|/ QH

Question 20

Explain the steps of the Carnot Cycle?

Answer 20

1-2 isothermal expansion
2-3 adiabatic expansion
3-4 isothermal compression
4-1 adiabatic compression

Question 21

Explain the steps of the Otto Cycle?

Answer 21

0-0'
1-2 adiabatic 
2-3 isothermal 
3-4 adiabatic 
4-5 isothermal

Question 22

What is a reversible heat engine and what are the applications?

Answer 22

A heat engine running backwards transfers heat from a cool reservoir to a hotter reservoir by doing work
Two main applications:
Refrigerators
Heat pumps

Question 23

What is the equation for the thermal energy of a gas?

Answer 23

U=fnRT/2=fNkbT/2

Question 24

Why more heat would be required under conditions of constant pressure than constant volume?

Answer 24

Cp > CV because a gas-heated at constant pressure will expand, and when it expands it does work, so you have to put in more energy.