KVPY Sample Paper KVPY Stream-SX Model Paper-25

Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of n moles having pressure \[{{P}_{0}}\] volume \[{{V}_{0}}\] and temperature \[{{T}_{0}}\] is

A) \[\frac{R}{{{P}_{0}}{{V}_{0}}}\]

B) \[\frac{{{P}_{0}}{{V}_{0}}}{R}\]

C) \[\frac{1}{{{T}_{0}}}\]

D) \[\frac{1}{n\,{{T}_{0}}}\]

Correct Answer: C

Solution :

\[PV=nRT\]

\[PdV=nRdT\]

\[\gamma =\frac{1}{V}\frac{dV}{dT}\]and \[\frac{dV}{dT}=\frac{nR}{P}\] \[\gamma =\frac{1}{T}\]

For given temperature \[{{T}_{0}},\] \[\gamma =\frac{1}{{{T}_{0}}}\]