In a given process on an ideal gas, $$dW = 0$$   and $$dQ < 0.$$   Then for the gas

Solution :
From the first law of thermodynamics
$$\eqalign{ & dQ = dU + dW \cr & {\text{Here}}\,dW = 0\,\left( {{\text{given}}} \right) \cr & \therefore dQ = dU \cr & {\text{Now}}\,{\text{since}}\,dQ < 0\,\left( {{\text{given}}} \right) \cr & \therefore dQ\,{\text{is}}\,{\text{negative}} \cr & \Rightarrow dU = - ve \Rightarrow dU\,{\text{decreases}}{\text{.}} \cr} $$
$$ \Rightarrow $$ Temperature decreases.