A) When heat is supplied to the gas its temperature will increase.
B) The coefficient of volume expansion of the gas equals\[\frac{-2}{T}\].
C) The molar heat capacity of the gas is\[2R\].
D) When heat is supplied to the gas its pressure increases.
Correct Answer: B
Solution :
[b] \[V{{T}^{2}}=\] constant \[\Rightarrow \,\,\,P{{V}^{3/2}}=\] constant \[C={{C}_{v}}+\frac{R}{1-n}=\frac{3R}{2}+\frac{R}{1-\frac{3}{2}}=-\frac{R}{2}\] C is negative therefore when heat is supplied to the gas, its temperature will decrease. \[V{{T}^{2}}=\] constant \[\Rightarrow \,\,\,\,\frac{\Delta V}{V}+2\frac{\Delta T}{T}=0\] Coefficient of volume expansion \[Y=\frac{\Delta V}{V\Delta T}=-\frac{2}{T}\] \[V{{T}^{2}}=\] constant \[\Rightarrow \,\,\,\frac{{{T}^{3}}}{P}=\] constant When heat is supplied, both temperature and pressure will decrease.
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