An ideal gaseous sample at initial state i (P_o, V_o, T_o) is allowed to expand to volume 2 V_o using two different process; in the first process the equation of process is 2PV²=K₁ and in second process the equation of the process is PV= K₂. Then,

Very difficult

A

Work done in first process will be greater than workdone in second process (magnitude wise)
B

The order of values of work done can not be compared unless we know the value of K₁ and K₂.
C

Value of work done (magnitude) in second process is greater than the work done in first process irrespective of the value of K₁ and K₂
D

1st process is not possible

Solution

Work done in adiabaticprocess
W = $\frac{K}{1 - γ} [V_{f}^{1 - γ} - V_{i}^{1 - γ}]$
Caluculation of work done in 1st Process:
2PV² = K₁
From the equation :
PV² = $\frac{K_{1}}{2}$ and $γ$ =2
W₁ = $\frac{K_{1}}{2 [1 - 2]} [V_{f}^{- 1} - V_{i}^{- 1}]$
W₁= $- \frac{K_{1}}{2} [V_{f}^{- 1} - V_{i}^{- 1}]$
Caluculation of work done in second process :
It is expansion work
PV¹ = K₂ ; $γ$ = 1
W₂ = $\frac{K_{2}}{1 - 1} [V_{i}^{1 - 1} - V_{f}^{1 - 1}] = \infty$
W₂ > W₁

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