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An ideal gas has pressure P at absolute temperature T. Its pressure is increased by $ΔP$ due to an increase in temperature $ΔT$ . If the volume of the gas remains constant, the fractional change in pressure per unit rise in temperature $(ΔP / P) / ΔT$ is proportional to

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$T$

$\sqrt{T}$

$1 / T$

$1 / \sqrt{T}$

answer is C.

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Detailed Solution

As the gas is ideal: $PV = nTR$ , and here V, n and R are constants. Hence if T changes, P changes. Introducing changes we get $V (P + ΔP) = n (T + ΔT) R$ . From this subtract $PV = nTR$ and manipulate for the quantity $(ΔP / P) / ΔT$

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