Discussion Forum

A reversible cyclic process for an ideal gas is shown below. Hence , P , V and T are pressure, volume and temperature respectively , The thermodynamic parameters q,w, H and U are heat, work, enthalpy and internal energy, respectively.

The correct options is (are)

Answer:

Explanation:

In the given curve AC represents isochoric process as volume at both the points is same i.e., V₁

Similarly , AB represents isothermal process ( as both the points are at T₁ temperature )  and BC represents  isobaric process as both the points are at p₂ pressure.

       Now (i) for option (a)

                          $q_{AC}=\triangle U_{BC}=nC_{v}(T_{2}-T_{1})$

where, n= number of moles,

     C_v= specific heat capacity at constant volume

   However, W_AB ≠ P₂ ( V₂ -V₁) instead 

            $w_{AB}=nRT_{1}ln(\frac{V_{2}}{V_{1}})$

   So, this option is incorrect.

(ii) For option (b)

           $q_{BC}=\triangle H_{AC}=nC_{p}(T_{2}-T_{1})$

   where , C_p= specific heat capacity at constant  pressure.

Likewise,

     $w_{BC}=-P_{2}(V_{1}-V_{2})$

Hence, the option is correct.

(iii)  For option (c)

        as $nC_{p}(T_{2}-T_{1})<nC_{v}(T_{2}-T_{1})$

So         $\triangle H_{CA}<\triangle U_{CA}$

 and    $q_{AC}=\triangle U_{BC}$

Hence, this option is also correct.

(IV)   For option (d)

         Although    $q_{BC}=\triangle H_{AC}$

    but  $\triangle H_{CA}>\triangle U_{CA}$

  Hence, this option is incorrect.