SATHEE: Thermodynamics Question 301

Thermodynamics Question 301

Question: The efficiency of an ideal gas with adiabatic exponent $‘ γ^{'}$ for the shown cyclic process would be

Options:

A) $\frac{(2 l n 2 - 1)}{γ / (γ - 1)}$

B) $\frac{(1 - 2 l n 2)}{γ / (γ - 1)}$

C) $\frac{(2 l n 2 + 1)}{γ / (γ - 1)}$

D) $\frac{(2 l n 2 - 1)}{γ / (γ + 1)}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $W_{A B} = 0, W_{B C} = P Δ V = n R Δ T = - n R T_{0}$

$W_{C A} = n R T ℓ n \frac{V_{f}}{V_{i}} = n R (2 T_{0}) ℓ n 2$

$Q_{B C} = n C_{p} Δ T = (\frac{n R γ}{γ - 1}) T_{0}$

$Efficieancy, η = \frac{W}{Q} = [\frac{2 ℓ n 2 - 1}{γ / (γ - 1)}]$

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