A certain amount of an ideal monoatomic gas undergoes a thermodynamic process such that `VT^(2)=` constat where `V=` volume of gas, `T=` temperature of gas. Then under process

Options

A. When heat is supplied to gas its temperature will increase
B. the coefficient of volume extension of gas equals `-(2)/(T)`
C. The molar heat capacity of gas is 2R
D. When heat is supplied to the gas its temperature decreases.

Answer

B, D

Explanation

`VT^(2)=coilPV^((3)/(2))=C`
`C=CV+(R)/(1-n)=(3R)/(2)+(R)/(1-(3)/(2))=-(R)/(2)`
C is negative no heat is supplied to gas temp decreases.
`VT^(2)=Cimplies(DeltaV)/(V)+(2DeltaT)/(T)=0`
`gamma=(DeltaT)/(VDeltaT)=-(2)/(T)`