SATHEE: Thermodynamics Question 303

Thermodynamics Question 303

Question: A monoatomic ideal gas goes through a process $p = p_{0} - α V$ where $p_{0}$ and $α$ are positive constants and V is its volume. At what volume will the entropy of gas be maximum?

Options:

A) $\frac{5 p_{0}}{6 α}$

B) $\frac{p_{0}}{2 α}$

C) $\frac{p_{0}}{4 α}$

D) $\frac{5 p_{0}}{8 α}$

Show Answer

Answer:

Correct Answer: D

Solution:

[d] $d s = n C_{v} d T + P d V = 0$

$n R \frac{d T}{d V} + (p_{0} - α V) = 0$

$p V = n R T$

$p_{0} V - α V^{2} = n R T$

$p_{0} - 2 α V = n R \frac{d T}{d V}$

$- (p_{0} - α V) (γ - 1) = p_{0} - 2 α V$

$- p_{0} (γ - 1) + α (γ - 1) V = p_{0} - 2 α V$

$p_{0} V = α V (γ + 1)$

$V = \frac{p_{0} γ}{α (γ + 1)}$

$V = \frac{p_{0} \times \frac{5}{3}}{α (\frac{5}{3} + 1)} = \frac{5 p_{0}}{8 α}$

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Thermodynamics Question 303

Question: A monoatomic ideal gas goes through a process p=p0−αV where p0 and α are positive constants and V is its volume. At what volume will the entropy of gas be maximum?

Options:

Answer:

Solution:

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Question: A monoatomic ideal gas goes through a process $p = p_{0} - α V$ where $p_{0}$ and $α$ are positive constants and V is its volume. At what volume will the entropy of gas be maximum?