Question

The network done on the gas in the cycle ABCDA is

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P - T diagram.

(a) zero 

(b) 276R

(c) 1076R 

(d) 1904R

Answer 1

(b) : Total work done on the gas when taking from A to B = 400R, from C to D is equal and opposite.
They cancel each other.
For taking from D to A, work done on the gas
= +414R.
Work done on the gas in taking it from B to C,pressure  is decreased, temperature remain the same, volume increases.
⇒ WBC + WDA = 2 ln 2(500R – 300R).
⇒ WBC + DA = (2 ln 2) × (200R)
= 400R × 0.693 = 277R.

Therefore, Work done along AB and CD cancel each other
because pressure changes but temperature is the same.
Network done on the gas of 2moles of helium through the whole network = 277R per cycle or nearest to the answer (b).