CAIE A-Level Physics 16.1 Internal Energy

Practise relating molecular kinetic and potential energies to internal energy, temperature changes and heating, cooling or phase-change processes.

Exam points

explain internal energy as a state property made from molecular kinetic and potential energies
relate temperature changes and heating/cooling to changes in internal energy

Covered syllabus points

16.1.1—Internal energy is determined by the state of the system and that it can be 16.1.2—Relate a rise in temperature of an object to an increase in its internal

[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: 3]

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

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 .

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

(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

All question bank results loaded

Covered syllabus points

16.1 Internal energy question 1

Question (a)

Question (i)

Question (b)

16.1 Internal energy question 2