Question

A monoatomic gas follows cyclic process ABCA, heat supplied to the gas in these steps are: for $AB\to x$, for $BC\to y$ and for $CA\to z$, then what is the efficiency of engine based on cyclic process ABCA.
(B and C lie on same isothermal curve)

• A. $\frac{x+y-z}{x+y}$
• B. $\frac{x+z-y}{x+z}$
• C. $\frac{y+z-x}{y+z}$
• D. $\frac{x+y+z}{x+y}$

Answer 1

The correct option is D $\frac{x+y+z}{x+y}$

For AB $Q_{AB}=+x$ (heat added)
For BC $Q_{BC}=\underset{\underset{0}{\downarrow }}{\Delta u}+\underset{\underset{+ve}{\downarrow }}{\Delta w}=+y$
For CA $Q_{CA}=z$ (but it is negative because heat is released)
So, during AB and BC, heat is supplied to the system.
Therefore, $Q_{in}=x+y$.
The work done by the sytem in a cylic process is summation of all the heat supplied.
So, work done ($W$)= $x+y+z$.

Efficiency = $\frac{W}{Q_{in}}=\frac{x+y+z}{x+y}$