Question

One mole of an ideal monoatomic gas undergoes a cyclic process. Process 1 → 2 is a quarter circle. If the efficiency of the cycle $(\pi = \frac{22}{7})$ is $\frac{N}{80}$, find $N$.

Answer 1

11

Answer 2

Using the internal–energy changes $U=\tfrac32PV$ we get $\Delta U_{1\to2}=9$. Parameterizing the quarter–circular process 1 → 2 (with the circle determined from its endpoints) gives a work of about 3.705 in L atm so that $Q_{1\to2}=9+3.705$. (The work for the other two processes is –2 (for 3 → 1) and zero (for 2 → 3).) Thus the net work is 1.705 and the efficiency is

$$\eta=\frac{1.705}{3.705+9}\approx 0.1341=\frac{11}{80}\,,$$

so that $N=11$.