Q: An ideal gas is subjected to cyclic process involving four thermodynamics states, the amount of heat (Q) and work (W) involved in each of these states :

Q_{1} = 6000 J, Q_{2} = – 5500 J; Q_{3} = – 3000 J; Q_{4} = 3500 J ; W_{1} = 2500 J; W_{2} = – 1000 J; W_{3} = – 1200 J; W_{4} = x J . The ratio of the net work done by the gas to the total heat absorbed by the gas is η . The values of x and η respectively are

(a) 500 ; 7.5%

(b) 700 ; 10.5%

(c) 1000 ; 21%

(d) 1500 ; 15%

Ans: (b)

Sol: In cyclic process

Q_{1} + Q_{2} + Q_{3} + Q_{4} = W_{1} + W_{2} + W_{3} + W_{4}

6000 – 5500 – 3000 + 3500 = 25 00 – 1000 – 1200 + x

x = 700 J

∆Q_{cyclic} = ∆W_{cyclic} = 1000 J

$\large \eta = \frac{\Delta W_{cyclic}}{Heat Supplied} = \frac{1000}{Q_1 + Q_4}$

$\large \eta = \frac{1000}{6000 + 3500} $

$\large \eta = \frac{10}{95} = \frac{10}{95} \times 100 $

= 10.5 %