One mole of an ideal gas at an initial temperature of TK does 6R Joule of work adiabatically. If the ratio of specific heat of this gas at constant pressure and at constant volume is `5/3`, the final temperature of gas will be ____

Options

A. (T-4)K
B. (T+2.4)K
C. (T-2.4)K
D. (T+4)K

Answer

A

Explanation

`T_1`=T,W=6R Joule , `gamma=5/3`
`W=(P_1V_1 -P_2V_2)/(gamma-1)`
`=(nRT_1-nRT_2)/(gamma-1) =(nR(T_1-T_2))/(gamma-1)`
`therefore 4=T-T_2`
`therefore T_2=(T-4)` K