Physics 9702 · AS & A Level · Equation of state

Equation of state — practice question

A sample holds a fixed quantity of gas. The gas has pressure $p$, volume $V$ and thermodynamic temperature $T$. Fig. 4.1 plots how $pV$ varies with $kT$ for the sample, where $k$ is the Boltzmann constant.
(a(i))[1]

State the value assigned to absolute zero on the Celsius temperature scale.

(a(ii))[1]

State the value of absolute zero on the thermodynamic temperature scale. Include a unit in your response.

(b(i))[1]

State what the variation shown in Fig. 4.1 indicates about the nature of the gas.

(b(ii))[2]

Determine how many molecules, $N$, are present in the gas sample.

(b(iii))[1]

Use your answer from (b)(ii) to find the amount $n$ of gas in the sample.

(c)[4]

When $pV$ is $270\,\text{J}$, the root-mean-square (r.m.s.) speed of the gas molecules is $1900\,\text{m s}^{-1}$. Find the mass, in $\text{u}$, of one molecule of the gas, where $\text{u}$ denotes the unified atomic mass unit.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: temperature is -273.15 ^{\circ}C

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