One mole of an ideal gas is allowed to expand reversibly and adibatically from a temperature of 27°C . If the work done during the process is 3 kJ , then final temperature of the gas is (C_v = 20 J/K)

Given number of moles = 1
Initial temperature = 27°C = 300K
Work done by the system = 3kJ = 3000J
It will be (-) because work is done by the system.
Heat capacity at constant volume (Cv) = 20 J/K
We know that work done
$\begin{array}{l}\mathrm{W}=-{\mathrm{nC}}_{\mathrm{V}}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right);3000=-1\times 20\left({\mathrm{T}}_2-300\right.\\ 3000=-20{\mathrm{T}}_2+6000\\ 20{\mathrm{T}}_2=3000;{\mathrm{T}}_2=\frac{3000}{20}=150\mathrm{K}\end{array}$