One mole of ideal gas goes through a process `pV^3 ` = Constant , where p and V are pressure and volume, respectively. Let W be the work done by the gas as its temperature is increased by `Delta T`.
The value of |W| is (R is the universal gas constant. )

Options

A. ` R Delta T`
B. `1/3 R Delta T`
C. `R^3 Delta T`
D. `R/2 Delta T`

Answer

D

Explanation

Key Idea For an adiabatic system , `pV ^(gamma)` = constant.
Given ,`pV^3` = constant , which shows the adiabatic process.
where, `gamma =3`
Work done in an adiabatic proccoss,
`W_(ad) = (p_1V_1-p_2V_2)/(gamma-1)`
Where `p_1 and p_2` are initial and final pressure and `V_1 and V_2` are the initial and final volume of a gas, respectively.
`rArr W_(ad) = (n RT_1-nRT_2)/(gamma-1) (because pV =nRT)`
`= (nR)/(gamma-1)(T_1-T_2)`
`rArr W_(ad)= (nR)/(3-1) DeltaT =(R DeltaT)/2 (because n=1)`