The ratio of work done by an ideal diatomic gas to the heat supplied by the gas in an isobaric process is ;

HINT:- An isobaric process is a type of thermodynamic process, in which the pressure of the system stays constant.

Solution:- Step 1:- Concept of Work dore and Heat for Isobaric process:-

for isobaric process pressure of the system remains constant. So for constant pressure Heal ' $\Delta Q$ ' is given dy -

$\Delta Q=n C_{p} \Delta T$

where $n \rightarrow n_{0}$ of moless of ideal gas $C_{p} \rightarrow$ molar theat copacity in constant piessure

$\Delta T \rightarrow$ chonge in temperature

Step 2:-Work done (W) to isobaric process is given by -

$\Delta W=p \Delta v$

where $P \rightarrow$ pressure of the gas (system)

$\Delta v \rightarrow$ change in volume

$\Delta w=P\left(\operatorname{ar} V_{2}-V_{1}\right)$

(Since pressure is constant)

$\begin{array}{l} \Delta W=P V_{2}-P V_{1} \quad\left(V_{2} \rightarrow\right. \text { final voluene } \\ V_{1} \rightarrow \text { initial volure, } \\ \Delta W=n R T_{2}-n R T_{1} \end{array}$

(By ideal gas equation $P V=n R T$ )

$\begin{array}{l} \Delta W=n R\left(T_{2}-T_{1}\right) \\ \Delta w=n R \Delta T \end{array}$

where $n \rightarrow$ no. of moles

$R \rightarrow$ universal gas constant

$T_{2} \rightarrow$ final temp.

$T_{1} \rightarrow$ initial terp.

step 3:- Calculating Ration :-

Ratio of Woxk dere to neat is given by

$\frac{W}{\theta}=\frac{n R \Delta T}{n C_{p} \Delta T}=\frac{R}{C_{p}}$

for diatonic gas $C_{p}$ is $\frac{7}{2} R$

Now

$\begin{array}{l} \frac{W}{Q}=\frac{R}{\frac{7}{2} R} \\ \frac{W}{Q}=\frac{2}{7} \end{array}$

option (c) is correct