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  • Give answer! Initial pressure and volume of a gas are P and V respectively. First it is expanded isothermally to volume 4V and then compressed adiabatically to volume V. The final pressure of gas will be

Initial pressure and volume of a gas are P and V respectively. First it is expanded isothermally to volume 4V and then compressed adiabatically to volume V. The final pressure of gas will be

  • Option 1)

    1P

  • Option 2)

    2P

  • Option 3)

    4P

  • Option 4)

    8P

 

Answers (1)

As we learnt in 

Equation of state -

dQ= 0

n\, C_{V}\, dT+PdV= 0
 

- wherein

On solving

\gamma \frac{dV}{V}+\frac{dP}{P}= 0

\Rightarrow PV^{\gamma }= constant

 

First process

PV= Constant

 PV= P_{1}\: 4V\ \, \, or\ \, \, P_{1}= \frac{P}{4}

Adiabatic compression

P_{1}V_{1}\gamma = P_{2}V_{2}\gamma\ \, \, or\ \: \: \frac{P}{4}(4V)^{\gamma}=P_{2}V^{\gamma}

P_{2}= \frac{P}{4}. (4^{\gamma})

\Rightarrow    \gamma is not given.

 


Option 1)

1P

Incorrect

Option 2)

2P

correct

Option 3)

4P

Incorrect

Option 4)

8P

Incorrect

Posted by

Vakul

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