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A monoatomic gas at a pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is : (take \(\large \gamma \) = 5/3)

(A)

64 P

(B)

32 P

(C)

P/64

(D)

16P

NEET - Medical UG-2014 Easy

Answer & Solution:

Incase of isothermal process  \(\large P_{1}V_{1}=P_{2}V_{2}\)

\(\large \Rightarrow PV=P_{2}(2V)\Rightarrow P_{2}=\frac{P}{2}\) 

Incase of adiabatic process \(\large P_{2}V_{2}^{\gamma }=P_{3}V_{3}^{\gamma }\) 

On applying values  \(\Large \frac{P}{2}2V^{\frac{5}{3}}=P_{3}(16V)^{\frac{5}{3}}\) 

\(\Large \Rightarrow P_{3}=\frac{P}{2}\times \left (\frac{1}{8} \right )^{\frac{5}{3}}=\frac{P}{64}\)    

 

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Chemistry Biology

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