Thermodynamics - Result Question 10

11. The volume $(V)$ of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

[2018]

(a) $\frac{2}{5}$

(b) $\frac{2}{3}$

(c) $\frac{2}{7}$

(d) $\frac{1}{3}$

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Answer:

Correct Answer: 11. (a)

Solution:

  1. (a) Gas is monatomic, so $C_p=\frac{5}{2} R$

Given process is isobaric

$\therefore dQ=nC_p dT$

$\Rightarrow dQ=n(\frac{5}{2} R) d T$

$dW=PdV=n$ RdT

$\therefore \quad$ Required ratio $=\frac{d W}{d Q}=\frac{n R d T}{n(\frac{5}{2} R) d T}=\frac{2}{5}$