First slide

First law of thermodynamics

Question

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

Easy

A

$\frac{2}{5}$
B

$\frac{2}{3}$
C

$\frac{1}{3}$
D

$\frac{2}{7}$

Solution

Given process is isobaric.
$∴ d Q = n C_{p} d T; where C_{p}$ is specific heat at constant pressure.
$or d Q = n (\frac{5}{2} R) d T$
$\begin{array}{l} Also, d W = P d V = n R d T \\ Required ratio = \frac{d W}{d Q} = \frac{n R d T}{n (\frac{5}{2} R) d T} = \frac{2}{5} \end{array}$

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