A rigid, frictionless piston contains an ideal gas occupying at a pressure of and a…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A rigid, frictionless piston contains an ideal gas occupying

0.10\,\text{m}^3

at a pressure of

2.0\times10^{5}\,\text{Pa}

and a temperature of

290\,\text{K}

. The gas is taken through the following sequence of changes: Step 1 (Constant-pressure expansion): It expands at its initial pressure until its volume becomes

0.15\,\text{m}^3

. Step 2 (Constant-volume cooling): Keeping the volume fixed at

0.15\,\text{m}^3

, the gas is cooled to a temperature of

280\,\text{K}

. (a) Calculate the temperature of the gas immediately after Step 1. (b) Determine the pressure of the gas after Step 2. (c) Compare the final pressure obtained in part (b) with the initial pressure and express the difference as a percentage of the initial value. Explain briefly how the two successive operations combine to produce this result.

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