During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio C_{P}/C_{V} for the gas is

  • Option 1)

    4/3\;

  • Option 2)

    \; 2\;

  • Option 3)

    \; 5/3\;

  • Option 4)

    \; 3/2

 

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

 

In the given question

P \propto T^{3}

or P T^{-3} = constant ......(1) 

From adiabatic equation

P^{1-\gamma } . T^{\gamma} = constant.....(2)

From equation 1 and 2

\frac{\gamma}{1-\gamma }= -3 \\ or 3\gamma -3=\gamma \\ or \ \gamma =3/2

\therefore \frac{C_p}{C_v}= \gamma = 3/2

 


Option 1)

4/3\;

The option is incorrect.

Option 2)

\; 2\;

The option is incorrect.

Option 3)

\; 5/3\;

The option is incorrect.

Option 4)

\; 3/2

The option is correct.

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