A mass of diatomic gas (\gamma =1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27^{o}C to 927^{o}C. The pressure of the gas in final state is: 

  • Option 1)

    28 atm      

  • Option 2)

    68.7 atm

  • Option 3)

    256 atm

  • Option 4)

    8 atm

 

Answers (1)
P Prateek Shrivastava

As 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 adiabatic process, p^{1 - \gamma }\cdot T^{\gamma }= \ constant

\Rightarrow {p_{i}}^{1-\gamma }\cdot {T_{i}}^{\gamma } = {p_{f}}^{1-\gamma }\cdot {T_{f}}^{\gamma }

\Rightarrow p_{f} = \left ( {p_{i}}^{1-\gamma } \cdot \frac{{T_{i}}^{\gamma }}{{T_{f}}^{\gamma }}\right )^{\frac{1}{1-\gamma }} = p_{i}\cdot \left ( \frac{T_{i}}{T_{f}} \right )^{\frac{\gamma }{1-\gamma }}

p_{i} = 2\ atm, \ \gamma = 1.4

T_{i} = 300\ K, \ T_{f} = 1200\ K

\Rightarrow p_{f} = \left ( 2\ atm \right )\left ( \frac{300}{1200} \right )^{\frac{1.4}{-0.4}} = 2\ atm\cdot \left ( 2^{7} \right )

p_{f} = 256\ atm


Option 1)

28 atm      

This option is incorrect

Option 2)

68.7 atm

This option is incorrect

Option 3)

256 atm

This option is correct

Option 4)

8 atm

This option is incorrect

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