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

Concept:

In case of Isobaric process,

 \(V α T\)

where V and T is volume and temperature of the gas respectively.

Whenever work is done by gas the volume of gas changes. It is calculated using the formula 

\(W=P\ ∆V\)

\(W=n\ R\ ∆T\)

where n is number of moles of gas, R= 8.314 J mol^-1K^-1 is gas constant , \(∆T\) is change in temperature.

If work is done by the system(gas) then heat is absorbed by it. Absorption of heat leads to change in the internal energy of the gas molecules.

Formula to calculate change in heat energy of gas is \(∆Q=n C_P ∆T\)

where n is number of moles of gas, \(C_P\) molar specific heat at constant pressure , \(∆T\) is change in temperature.

Value of \(C_P\) for monoatomic gas molecule is \(\frac{5R}{2}\)

Calculation:

Volume of a monatomic gas = V

 Temperature = T

Given process is isobaric,

Heat absorbed by the gas,

dQ = n C_p dT

Value of \(C_P\) for monoatomic gas molecule is \(\frac{5R}{2}\)

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

Work done by the gas,

dW = P dV = n RdT

Required ratio \(= \frac{{dW}}{{dQ}} = \frac{{nRdT}}{{n\left( {\frac{5}{2}R} \right)dT}} = \frac{2}{5}\)