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  • The temperature of n moles of an ideal gas is increased from T to 3T in a process in which the temperature changes with volume as <img alt="\mathrm{T=k V^2}" src="https://entrancecorner.oncodecogs.

The temperature of n moles of an ideal gas is increased from T to 3T in a process in which the temperature changes with volume as \mathrm{T=k V^2} where k is a constant. The work done by the gas in this process is

Option: 1

n R T


Option: 2

2 n R T


Option: 3

\mathrm{\frac{3}{2} n R T}


Option: 4

3 n R T


Answers (1)

best_answer

\mathrm{\text { Given } T=k V^2 \text {. Therefore } d T=2 k V d V \text { or }}

\mathrm{d V=\frac{d T}{2 k V}}

\mathrm{\text { Also } P V=n R T \Rightarrow P=\frac{n R T}{V}}

\mathrm{\therefore \text { Work done } w=\int_T^{3 T} P d V}

\mathrm{\begin{aligned} & =\int_T^{3 T}\left(\frac{n R T}{V}\right) \times\left(\frac{d T}{2 k V}\right) \\ & =\int_T^{3 T} \frac{n R T d T}{2 k V^2} \\ & =\frac{n R}{2} \int_T^{3 T} d T \quad\left(\because k V^2=T\right) \\ & =n R T \end{aligned}}

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Ajit Kumar Dubey

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