One mole of a monatomic ideal gas at $300 K$ and $10 L$ (state A) undergoes a cycle: A to B, reversible isothermal expansion to $30 L$ ; B to C, isobaric compression to $10 L$ ; C to A, isochoric heating back to state A. Taking $R = 8.314 J mo l^{- 1} K^{- 1}$ , find the net work done by the gas in one cycle, in J (nearest integer).

Numerical answer type, answer in J, tolerance 1.

Answer: 1077 J

A to B:

w_{b y} = RT ln 3 = 2740.2 J

. At C,

V

is one third of that at B at the same pressure, so

T_{C} = 100 K

; B to C:

w_{b y} = P Δ V = R (T_{C} - T_{B}) = - 1662.8 J

. C to A is isochoric, work

0

. Net

= 2740.2 - 1662.8 = 1077.4 J

, about 1077 J.