Physics 9702 · AS & A Level · The first law of thermodynamics

The first law of thermodynamics — practice question

The volume of an ideal gas inside a cylinder is $1.80 \times 10^{-3}\,\text{m}^3$ when the pressure is $2.60 \times 10^5\,\text{Pa}$ and the temperature is $297\,\text{K}$, as shown in Fig. 2.1. The thermal energy needed to increase the temperature by $1.00\,\text{K}$ of $1.00\,\text{mol}$ of the gas at constant volume is $12.5\,\text{J}$. The gas is then heated at constant volume so that the internal energy of the gas rises by $95.0\,\text{J}$.
(a(i)(1))[2]

Calculate the quantity of gas, in $\text{mol}$, in the cylinder.

(a(i)(2))[2]

Calculate the increase in temperature of the gas.

(a(ii))[1]

Use your answer to (i) part 2 to demonstrate that the final pressure of the gas in the cylinder is $2.95 \times 10^5\,\text{Pa}$.

(b)[3]

The gas is now permitted to expand. No thermal energy enters or leaves the gas. While expanding against the external pressure, the gas does $120\,\text{J}$ of work. State and explain whether the final temperature of the gas is above or below $297\,\text{K}$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Application of $pV = nRT$

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