The molar specific heat of the process $$P=aT$$ for a monoatomic gas, a being constant , is $$b2R$$. The value of b is

We know that $$dQ=dU+dWspecific$$ heat $$C=dQdT=dUdT+dWdT$$ .......$$(i)Since$$, $$dU=CVdT$$ ..........$$(ii)C=CV+dWdT=CV+pdVdTpV=RT$$∴ For the given process, $$V=RTp=RT2adVdT=2RTa$$∴$$C=CV+p2RTa=CV+2R=32R+2R=72R$$

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The molar specific heat of the process $P = \frac{a}{T}$ for a monoatomic gas, a being constant , is $\frac{b}{2} R$ . The value of b is

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Solution

We know that
$\begin{array}{l} dQ = dU + dW \\ specific heat C = \frac{dQ}{dT} = \frac{dU}{dT} + \frac{dW}{dT} . . . . . . . (i) \\ Since, dU = C_{V} dT . . . . . . . . . . (ii) \\ C = C_{V} + \frac{dW}{dT} \\ = C_{V} + \frac{pdV}{dT} \\ pV = RT \\ ∴ For the given process, V = \frac{RT}{p} = \frac{{RT}^{2}}{a} \\ \frac{dV}{dT} = \frac{2 RT}{a} \end{array}$
$\begin{array}{l} ∴ C = C_{V} + p (\frac{2 RT}{a}) \\ = C_{V} + 2 R \\ = \frac{3}{2} R + 2 R = \frac{7}{2} R \end{array}$

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Thermodynamic processes

Remember concepts with our Masterclasses.

The molar specific heat of the process P=aT for a monoatomic gas, a being constant , is b2R. The value of b is

We know that dQ=dU+dWspecific heat C=dQdT=dUdT+dWdT .......(i)Since, dU=CVdT ..........(ii)C=CV+dWdT=CV+pdVdTpV=RT∴ For the given process, V=RTp=RT2adVdT=2RTa∴C=CV+p2RTa=CV+2R=32R+2R=72R

Ready to Test Your Skills?

free study material

The molar specific heat of the process $P = \frac{a}{T}$ for a monoatomic gas, a being constant , is $\frac{b}{2} R$ . The value of b is