A gas expands in such a way that its pressure and volume satisfy the condition PV² = constant. Then the temperature of the gas (a) will decrease. (b) will increase. (c) will not change. (d) may increase or decrease depending upon the values of pressure and volume.

Answer: (a). PV = nRT and PV² = C give PV = C/V, so T = C/nRV, i.e. T ∝ 1/V. The gas expands ( V increases), so T decreases. So the answer is (a) will decrease.

A gas expands in such a way that its pressure and volume satisfy the… | MHT CET 2024 (3 May, Shift 2)

Q127MHT CET 2024 · 3 MAY · SHIFT 2Medium

Thermodynamic Processes

A gas expands in such a way that its pressure and volume satisfy the condition $PV^{2} =$ constant. Then the temperature of the gas

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Answer: (a)

$PV = nRT$ and $PV^2 = C$ give $PV = \frac{C}{V}$ , so $T = \frac{C}{nRV}$ , i.e. $T \propto \frac{1}{V}$ .
The gas expands ( $V$ increases), so $T$ decreases.
So the answer is (a) will decrease.

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