Question

A gas is heated at a constant pressure. The fraction of heat supplied used for external work is :

• A. $\frac{1}{\gamma }$
• B. $(1-\frac{1}{\gamma })$
• C. $\gamma -1$
• D. $(1-\frac{1}{{\gamma }^2})$

Answer 1

The correct option is B $(1-\frac{1}{\gamma })$

At constant pressure,
Heat absorbed $=\Delta Q=n{C}_p\Delta T$,
Internal energy change $=\Delta U=n{C}_v\Delta T$
Required fraction $=\frac{\Delta W}{\Delta Q}=1-\frac{\Delta U}{\Delta Q}=1-\frac{C_v}{C_p}=1-\frac{1}{\gamma }$