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

Solution

Given process is isobaric.

$\therefore dQ=n{C}_{p}dT;\text{where}{C}_{p}$ is specific heat at constant pressure.

$\text{or}dQ=n\left(\frac{5}{2}R\right)dT$

$\begin{array}{l}\text{Also,}dW=PdV=nRdT\\ \text{Required ratio}=\frac{dW}{dQ}=\frac{nRdT}{n\left(\frac{5}{2}R\right)dT}=\frac{2}{5}\end{array}$

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