Chemistry - Thermodynamics - 1 Question with Solution | TestHub

In an isothermal process, temperature is constant

${\mathrm{T}}_2={\mathrm{T}}_1$

Area under P - V graph is more is isothermal

${\mathrm{W}}_{\text{isothermal}}>{\mathrm{w}}_{\text{adiabatic}}$

Now$\mathrm{\Delta }{\mathrm{U}}_{\text{isothermal}}=\mathrm{ }0$

In adiabatic${\mathrm{T}}_1{{\mathrm{V}}_1}^{\mathrm{\gamma }-1}={\mathrm{T}}_3{{\mathrm{V}}_3}^{\mathrm{\gamma }-1}$

$\frac{{\mathrm{T}}_3}{{\mathrm{T}}_1}={\left(\frac{{\mathrm{V}}_1}{{\mathrm{V}}_3}\right)}^{\mathrm{\gamma }-1}$

${\mathrm{T}}_3<{\mathrm{T}}_1$Hence internal energy decreases

$\mathrm{\Delta }{\mathrm{U}}_{\text{isothermal}}>\mathrm{\Delta }{\mathrm{U}}_{\text{adiabatic}}$