IB Physics SL B.3 Gas laws questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

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Question 1

Multiple choiceHard1 mark

A sample of $6.0 \times 10^{23}$ particles of a monatomic gas is initially at $400\ \mathrm{K}$ In a final state, its volume is twice its initial volume, its number density is $3/4$ of the initial value, and its temperature is $2/3$ of the initial value. At both states the gas is sufficiently hot and dilute for the ideal-gas approximation to apply. What is its final internal energy? Take $k_B=1.38 \times 10^{-23}\ \mathrm{J\,K^{-1}}$

Show answer and explanation

Answer: C. The particle-number ratio is the number-density ratio multiplied by the volume ratio: $N_f/N_i=(3/4)(2)=3/2$ Since $U=\frac{3}{2}Nk_BT$ the internal-energy ratio is $(3/2)(2/3)=1$ Thus $U_f=U_i=\frac{3}{2}(6.0\times10^{23})(1.38\times10^{-23})(400)=4.968\times10^3\ \mathrm{J}$ or $5.0\times10^3\ \mathrm{J}$ to two significant figures.
A: treats the number-density ratio as the particle-number ratio, omitting the volume change.
B: accounts for the temperature change but holds the particle number fixed.
D: treats the volume ratio as the particle-number ratio, ignoring the number-density change.
Remember: for an ideal monatomic gas, internal energy depends on particle number and absolute temperature.

Question 2

Paper 2Hard10 marks

A fixed amount of gas is measured in a cylinder with a movable piston. Figure 1 shows the measured pressure–volume states of the gas at two temperatures. The temperatures are in kelvin. $X$ is a further state of the same gas, at an unrecorded temperature. No curves have been fitted to the measurements.

(a)

Describe the pressure–volume relationship indicated by the $300\ \mathrm{K}$ measurements.

[1]

(b)

For the measurements at $V=2.00\ \mathrm{L}$ calculate $PV/T$ at each temperature. Give an appropriate unit.

[2]

(c)

A fixed amount of gas changes from state 1 $(P_1,V_1,T_1)$ to state 2 $(P_2,V_2,T_2)$ Using the empirical pressure–temperature law at constant volume and Boyle’s law at constant temperature, derive a relation between these two states. Temperatures are in kelvin.

[2]

(d)

A controller is expected to switch when the gas reaches $750\ \mathrm{K}$ Use state $X$ and both calibration results from part (b) to estimate the temperature at $X$ and decide whether the controller’s reported temperature is consistent with the measurements. Show your working.

[5]

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