In an adiabatic change, the pressure and temperature of a monoatomic gas are related with relation as `P prop T^(C )`, Where `C` is equal to:

Options

A. `5/2`
B. `2/5`
C. `3/5`
D. `5/3`

Answer

A

Explanation

It is given that `PpropT^(c)" "...(1)`
For an adiabatic change, `P^(1-gamma)T^(gamma)="constant"`
`thereforeP^(1-gamma)prop1/T^(gamma)orPpropT^(gamma/(gamma-1)" "...(2)`
and for the monoatomic gas, `gamma=5/3`
Comparing (1) and (2), we get
`c=gamma/(gamma-1)` but `gamma=5/3`
`thereforec=(5/3)/(5/3-1)=(5/3)/(2/3)=5/3xx3/2=5/2`