Chemistry - Thermodynamics - I Question with Solution | TestHub

From first law of thermodynamics, $$\Delta \mathrm{U}=\mathrm{q}+\mathrm{W}$$ In adiabatic expansion, $q=0$ $$\therefore \Delta \mathrm{U}=\mathrm{W}$$ During expansion of a gas $w$ is negative i.e $w<0$ or $\Delta \mathrm{U}<0$. We know that, $\Delta \mathrm{U}={\mathrm{nC}}_{\mathrm{V}}\Delta \mathrm{T}$ $$\begin{array}{lclc}\therefore & {\mathrm{nC}}_{\mathrm{V}}\Delta \mathrm{T}<0& \text{ or }& \Delta \mathrm{T}<0\\ \therefore & {\mathrm{T}}_{\mathrm{C}}-{\mathrm{T}}_{\mathrm{A}}<0& \text{ or }& {\mathrm{T}}_{\mathrm{C}}<{\mathrm{T}}_{\mathrm{A}}\end{array}$$ Thus, option (4) is incorrect while the remaining options are correct.