CAIE A-Level Physics 16.1.2 Temperature Rise and Internal Energy

Practise relating temperature change to molecular kinetic energy and internal-energy change, interpreting heating and cooling as energy changes in a system.

Exam points

relate a rise in an object’s temperature to an increase in its internal energy
interpret heating or cooling as a change in the internal energy of the system

[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

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16.1.2—Relate a rise in temperature of an object to an increase in its internal question 1