A gas at 1 atm, 10 litres and 300 K is heated at constant volume to 3 atm and then at constant pressure to 1800 K. It is then cooled at constant volume to 1 atm and then at constant pressure to its or

Question

A gas at 1 atm, 10 litres and 300 K is heated at constant volume to 3 atm and then at constant pressure to 1800 K. It is then cooled at constant volume to 1 atm and then at constant pressure to its original volume. C v ​ = 20.8 J m o l − 1 K − 1 . Find the total work done by the gas in the cycle in joules (nearest integer). Use 1 atm = 1.013 × 1 0 5 Pa.

TestHub · Accepted Answer

n = 8.314 × 300 1.013 × 1 0 5 × 0.01 ​ = 0.4061 mol, C p ​ = 29.1 . Heat in: n C v ​ ( 900 − 300 ) + n C p ​ ( 1800 − 900 ) = 15711 J. Cooling: 3 atm to 1 atm at constant volume gives 600 K; then to 300 K at 1 atm. Heat out: n C v ​ ( 1800 − 600 ) + n C p ​ ( 600 − 300 ) = 13685 J. W = Q in ​ − Q o u t ​ = 2026 J. (Check: loop area = ( 3 − 1 ) × 1.013 × 1 0 5 × 0.01 = 2026 J.)

Physics - Heat & Thermo Question with Solution | TestHub

Doubts & Discussion