Show that the final volume of the gas is about 53 m³.

Calculate, in J, the work done by the gas during this expansion.

Determine the thermal energy which enters the gas during this expansion.

Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.

Outline the change in entropy of the gas during the cooling at constant volume.

There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.

ALTERNATIVE 1

«Using \(\frac{{{V_1}}}{{{T_1}}} = \frac{{{V_2}}}{{{T_2}}}\)»

V₂ = \(\frac{{47.1 \times (273 + 19)}}{{(273 - 12)}}\)

V₂ = 52.7 «m³»

ALTERNATIVE 2

«Using PV = nRT»

V = \(\frac{{243 \times 8.31 \times (273 + 19)}}{{11.2 \times {{10}^3}}}\)

V = 52.6 «m³»

[2 marks]

W «= PΔV» = 11.2 × 10³ × (52.7 – 47.1)

W = 62.7 × 10³ «J»

Accept 66.1 × 10³ J if 53 used

Accept 61.6 × 10³ J if 52.6 used

[2 marks]

ΔU «= \(\frac{3}{2}\)nRΔT» = 1.5 × 243 × 8.31 × (19 – (–12)) = 9.39 × 10⁴

Q «= ΔU + W» = 9.39 × 10⁴ + 6.27 × 10⁴

Q = 1.57 × 10⁵ «J»

Accept 1.60 × 10⁵ if 66.1 × 10³ J used

Accept 1.55 × 10⁵ if 61.6 × 10³ J used

[3 marks]

concave curve from RHS of present line to point above LHS of present line

vertical line from previous curve to the beginning

[2 marks]

energy is removed from the gas and so entropy decreases

OR

temperature decreases «at constant volume (less disorder)» so entropy decreases

OWTTE

[1 mark]

different paradigms/ways of thinking/modelling/views

allows testing in different ways

laws can be applied different situations

OWTTE

[1 mark]