Thermodynamics (DP IB Physics: HL): Exam Questions

A system of particles in a gaseous state in the chamber of a piston has 2400 possible microstates. 

Calculate its microscopic entropy in units of eV K⁻¹.

The system is reset to another state with a different number of microstates. During a thermodynamic process, the number of microstates increases. 

Calculate the factor by which the number of microstates increased if the entropy increased by 1.6 × 10⁻⁴ eV K⁻¹.

The same system then undergoes isothermal expansion.

The gas applies a force of 140 N to a load, lifting it 20 cm vertically.

Calculate the heat transferred to the system.

The isothermal process occurs at 300 °C. 

Calculate its entropy change. 

An engineer is performing tests on a sample of helium gas (He).

Explain how the pV diagram shows that the internal energy changes during the adiabatic process from A to B.

The grey dashed lines represent isotherms.

In the diagram in part (a), point B has coordinates (300 kPa, 0.065 m³).

Calculate the number of moles of gas in the system.

The volume at point A in the adiabatic process is 0.083 m³.

Calculate the pressure at point A.

Explain why the calculation in part (c) would not be valid if the gas was water vapour.

The pV diagram shows a Carnot cycle for 3 moles of a monatomic ideal gas.

Describe the work done, change in internal energy and thermal energy transfer in each of the processes:

(i) 1 ⇒ 2

(ii) 2 ⇒ 3

(iii) 3 ⇒ 4

(iv) 4 ⇒ 1

State the name of each process throughout this cycle. 

The shaded space X has an area of 230.

Calculate the change in temperature in process 4 → 1.

Outline a similarity and a difference between the Clausius and Planck-Kelvin versions of the second law of thermodynamics.

A student draws an energy flow diagram to represent heat flow in a refrigerator.

State and explain, in terms of entropy, why this process violates the second law of thermodynamics.

Draw and label an arrow on the diagram to correct the student's diagram.

An idealised refrigerator cycle is shown on the pressure-volume diagram below.

(i) Draw arrows on the diagram to show the direction of the cycle.

[1]

(ii) Explain why this direction of the cycle allows heat to be removed from a cold region.

[2]

One mole of an ideal gas is taken through a cycle that consists of four processes:

• Isothermal expansion

• Adiabatic expansion

• Isothermal compression

• Adiabatic compression

This cycle is shown below.

The following unit conversions may be helpful:

1 L = 0.001 m³

1 atm = 101.3 kPa

Calculate

(i) the temperature at which isothermal compression occurs

[2]

(ii) the temperature at which isothermal expansion occurs.

[2]

State three assumptions made in order to calculate the answers to part (a) of this question.

Determine the efficiency of this cycle.

The coefficient of performance is the ratio of useful energy output to work input. 

In one instance, a refrigerator is used to cool food. The same equipment can also be used as a heat pump to heat a room.

Suggest why the same equipment has different coefficients of performance in these two scenarios. 

A refrigerator removes heat from a small space at a rate of 50 W and transfers 1.5 kWh to the room each day. 

Calculate its coefficient of performance, K.

The diagram shows a process which is not physically possible.

Explain how the process violates the Kelvin and Clausius statements of the second law. 

A newly designed heat engine operates using water vapour, which is triatomic. 

The equation used to model adiabatic processes for triatomic gases is:

Here, p  represents pressure, V  represents volume and k  is a constant. 

For this form of the adiabatic equation, the work done during an adiabatic process is given by the equation:

A gas is in an initial state 1, with a pressure of 301 kPa and volume of 0.0104 m³. It expands adiabatically to state 2 with a volume of 0.0520 m³.

Calculate the work done by the gas in this process.

Under these conditions, water vapour behaves very closely to an ideal gas.

The process in part (a) forms part of a Carnot cycle.

Show that the efficiency η  is given by:

,

where p₁ and p₂ are the pressures of states 1 and 2 respectively, and V₁ and V₂ are the volumes of states 1 and 2 respectively.

An engineering company are trying to advertise the heat engine from parts (a) and (b). Their marketing department produce an image for the website as part of the specifications of the heat engine.

Explain why this diagram is incorrect.

Two identical containers, A and B, are filled with the same gas, with the exact same initial conditions. 

Both containers are supplied with heat Q. In container A, the subsequent process is isobaric. In container B, the subsequent process is isovolumetric. 

State and explain which container of gas has the lowest final temperature.

The gases in containers A and B are reset to their identical initial states.

This time, the gas in A receives more heat than the gas in B, but both experience the same increase in temperature.

State and explain which gas absorbs heat at constant pressure and which gas absorbs heat at constant volume. 

Molar specific heat capacity at constant pressure is the thermal energy required to raise the temperature of one mole of an ideal gas by 1 K at constant pressure.

Molar specific heat capacity at constant volume is the thermal energy required to raise the temperature of one mole of an ideal gas by 1 K at constant volume.

Using the first law of thermodynamics, show that the gas constant  is