Physics 9702 · AS & A Level · Equation of state

Equation of state — practice question

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

State the value for absolute zero on the Celsius temperature scale.

(a(ii))[1]

State the value of absolute zero on the thermodynamic temperature scale, and include a unit in your answer.

(b(i))[1]

State what the change shown in Fig. 4.1 tells you about the gas.

(b(ii))[2]

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

(b(iii))[1]

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

(c)[4]

The root-mean-square (r.m.s.) speed of the molecules of the gas is $1900\,\text{m s}^{-1}$ when $pV$ is equal to $270\,\text{J}$. Determine the mass, in $u$, of one molecule of the gas, where $u$ is 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 = -273.15^{\circ}C

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