CAIE A-Level Physics 16 Thermodynamics

Practise relating internal energy to temperature and molecular energy, calculating gas work with signs and applying the first law to heat and energy change.

Exam points

interpret internal energy as a state quantity and relate it to temperature and molecular energy
calculate work in constant-pressure gas changes with correct sign conventions
apply the first law to connect heat, work and internal-energy change in thermodynamic processes

Covered syllabus points

16.1 Internal energy 16.2 The first law of thermodynamics

[Maximum number: 4]

(a)

A sample of $0.26 \mathrm{~m}^{3}$ of an ideal gas is at pressure $2.0 \times 10^{5} \mathrm{~Pa}$ and temperature 290 K .

Determine:

[ 2 ]

(i)

the internal energy of the gas. Explain your reasoning.
internal energy =

[ 2 ]

internal energy = total KE + PE of molecules

or

PE = 0 so internal energy = total KE of molecules

B1

internal energy $=1.3 \times 10^{25} \times 6.0 \times 10^{-21}$ $=7.8 \times 10^{4} \mathrm{~J}$

A1

(b)

The volume V of the gas in (b) is now varied, keeping its pressure constant.

On Fig. 3.1, sketch the variation with V of the internal energy U of the gas.

Fig. 3.1

[ 2 ]

[Maximum number: 7]

(a)

By referring to both kinetic energy and potential energy, explain what is meant by the internal energy of an ideal gas.

[ 2 ]

(b)

A fixed mass of an ideal gas at a temperature of $20^{\circ} \mathrm{C}$ is sealed in a cylinder by a piston, as shown in Fig. 2.1.

Fig. 2.1

The initial volume of the gas is $1.24 \times 10^{-4} \mathrm{~m}^{3}$ .
Thermal energy is supplied to the gas and its volume increases by $5.20 \times 10^{-5} \mathrm{~m}^{3}$ .

[ 2 ]

(i)

The piston is freely moving so that the gas is always at atmospheric pressure.

Atmospheric pressure is $1.01 \times 10^{5} \mathrm{~Pa}$ .
Calculate the work done by the gas.
work done by gas = J

[ 2 ]

$W=p \Delta V$

C1

$\begin{aligned} =1.01 \times 10^{5} \times 5.20 \times 10^{-5} =(+) 5.25 \mathrm{~J} \end{aligned}$

A1

(c)

The gas in (b) is allowed to return to its starting temperature. The piston is now fixed in position.

Thermal energy is supplied to increase the temperature to the same final temperature as in (b).
Use the first law of thermodynamics to suggest and explain how the specific heat capacity of the gas for this situation compares with the value in (b)(iii).

[ 3 ]

[Maximum number: 7]

A cylinder contains 5.12 mol of an ideal gas at pressure $5.60 \times 10^{5} \mathrm{~Pa}$ and volume $3.80 \times 10^{-2} \mathrm{~m}^{3}$ .

(a)

The average kinetic energy $E_{\mathrm{K}}$ of a molecule of the gas is given by the expression

E_{\mathrm{K}}=\frac{3}{2} k T

where k is the Boltzmann constant and T is the thermodynamic temperature.
The gas is heated at constant pressure so that its temperature rises by 125 K .

[ 3 ]

(i)

Calculate the increase in internal energy of the gas. Explain your working.

[ 3 ]

(for ideal gas,) change in internal energy is change in (total) kinetic energy (of molecules)

B1

$\Delta U=(3 / 2) \times 1.38 \times 10^{-23} \times 125 \times 5.12 \times 6.02 \times 10^{23}$

C1

$\Delta U=7980 \mathrm{~J}$

A1

(b)

Use the information in (b)(i) to calculate the external work done during the expansion of the gas.

work done =J [2]

[ 2 ]

$W=p \Delta V$

C1

$\begin{aligned} W=5.60 \times 10^{5} \times(4.75-3.80) \times 10^{-2} W=5320 \mathrm{~J} \end{aligned}$

A1

(c)

Use the first law of thermodynamics to determine the total thermal energy transferred to the gas in (b). Explain your reasoning.
energy = J

[ 2 ]

work done on the gas is negative or work is done by the gas

B1

increase in internal energy = thermal energy transferred to gas + work done on gas so thermal energy transferred to gas =7980-(-5320)

$=13300 \mathrm{~J}$

A1

All question bank results loaded

Covered syllabus points

16. Thermodynamics question 1

Question (a)

Question (i)

Question (b)

16. Thermodynamics question 2

Question (a)

Question (b)

Question (i)

Question (c)

16. Thermodynamics question 3

Question (a)

Question (i)

Question (b)

Question (c)