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‘n’ moles of an ideal gas undergoes a process A→B as shown in the figure.  The maximum temperature of the gas during the process will be :

  • Option 1) (9P0V0/4nR) 
  • Option 2) (3P0V0/2nR)  
  • Option 3) (9P0V0/2nR)  
  • Option 4)(9P0V0/nR)  

Answers (1)


As we learnt in

Ideal gas equation -

PV = nRT


- wherein

T= Temprature

P= pressure of ideal gas

V= volume

n= numbers of mole

R = universal gas constant


 At any point between A & B we can write relation between P & V by using equation of straight line



P\left(\frac{-V_{0}}{P_{0}} \right )+2V_{0}=V-V_{0}


From ideal gas equation 

    PV = nRT

\Rightarrow\ \;\frac{nRT}{V}=\frac{-P_{0}}{V_{0}}(V-3V_{0})


For temperature to be maximum at any point \frac{dT}{dV}=0

\Rightarrow\ \;2V-3V_{0}=0

    \therefore\ \; V=\frac{3V_{0}}{2}

\therefore\ \; T_{max}=\frac{-P_{0}}{nRV_{0}} \left(\frac{9}{4}V_{0}^{2}-\frac{9}{2}V_{0}^{2} \right )=-\frac{P_{0}}{nRV_{0}}.\frac{-9}{4}V_{0}^{2}=\frac{9}{4}\frac{P_{0}V_{0}}{nR}

Correct option is 1.



Option 1)


This is the correct option.

Option 2)


This is an incorrect option.

Option 3)


This is an incorrect option.

Option 4)


This is an incorrect option.

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