Physics 9702 · AS & A Level · The first law of thermodynamics
The first law of thermodynamics — practice question
An ideal gas occupies a volume of $3.1 \times 10^{-3}\,\text{m}^3$ at a pressure of $8.5 \times 10^5\,\text{Pa}$ and a temperature of $290\,\text{K}$, as illustrated in Fig. 2.1. The gas then undergoes a sudden expansion to a volume of $6.3 \times 10^{-3}\,\text{m}^3$. No thermal energy is transferred during this expansion. Afterward, the gas has a pressure of $2.7 \times 10^5\,\text{Pa}$ and a temperature of $T_F$, as shown in Fig. 2.1.
(a)[3]
Demonstrate that the gas contains $6.6 \times 10^{23}$ molecules.
(b(i))[1]
Demonstrate that the gas has a final temperature $T_F$ of $190\,\text{K}$.
(b(ii))[3]
The mean translational kinetic energy $E_k$ of one molecule of an ideal gas is $E_k = \frac{3}{2}kT$, where $T$ is the thermodynamic temperature and $k$ is the Boltzmann constant. Calculate the rise in internal energy $\Delta U$ of the gas.
(c)[2]
Apply the first law of thermodynamics to show why the external work $w$ done on the gas during the expansion equals the increase in internal energy found in (b)(ii).
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Application of the ideal gas equation $pV=nRT$ or $pV=NkT$” …