DP Physics (last assessment 2024)

Question 18M.3.SL.TZ1.7a

[Maximum mark: 2]

18M.3.SL.TZ1.7a

The pressure–volume (pV) diagram shows a cycle ABCA of a heat engine. The working substance of the engine is 0.221 mol of ideal monatomic gas.

At A the temperature of the gas is 295 K and the pressure of the gas is 1.10 × 10⁵ Pa. The process from A to B is adiabatic.

(a)

Show that the pressure at B is about 5 × 10⁵ Pa.

[2]

Markscheme

« ${p_1}V_1^{\frac{5}{3}} = {p_2}V_2^{\frac{5}{3}}$ »

$1.1 \times {10^5} \times {5^{\frac{5}{3}}} = {p_2} \times {2^{\frac{5}{3}}}$

p₂ «= $\frac{{1.1 \times {{10}^5} \times {5^{\frac{5}{3}}}}}{{{{2.5}^{\frac{5}{3}}}}}$ » = 5.066 × 10⁵ «Pa»

Volume may be in litres or m³.

Value to at least 2 sig figs, OR clear working with substitution required for mark.

[2 marks]

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