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  • moles of an ideal gas are made to undergo a linear process <img alt="\mathrm{A-B}" src="https://entra

\mathrm{N} moles of an ideal gas are made to undergo a linear process \mathrm{A-B} shown on the \mathrm{ P-V} diagram. The temperature will be maximum when volume is


 

Option: 1

\mathrm{V_0}

 


Option: 2

\mathrm{2 \mathrm{~V}_0}
 


Option: 3

\mathrm{3 V_0 / 4}
 


Option: 4

3 \mathrm{~V}_0 / 2


Answers (1)

best_answer

Hints: \mathrm{\frac{y-y_1}{y_1-y_2}=\frac{x-x_1}{x_1-x_2}}

\mathrm{ \Rightarrow \frac{P-P_0}{P_0-P_0 / 2}=\frac{V-V_0}{V_0-2 V_0} }

\mathrm{ \Rightarrow P=\frac{3 P_0}{2}-\frac{P_0 V}{2 V_0}}

\mathrm{ \Rightarrow \frac{N R T}{V}=\frac{3 P_0}{2}-\frac{P_0 V}{2 V_0} }

\mathrm{ \Rightarrow T=\frac{3 P_0}{2 N R} V-\frac{P_0 V^2}{2 N R V_0} }

\mathrm{ \Rightarrow T=\text { to be maximum, } \frac{d T}{d V}=0}

Hence option 4 is correct.







 

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