A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be

Step-by-step solution

Change in entropy is given by d S = d Q T . Since, the process is d S = 0 , d Q = 0 . Therefore, constant entropy means the process is adiabatic. P V γ = constant ⇒ P 1 V 1 γ = P 2 V 2 γ For a monatomic gas γ = 5 3 ⇒ P 1 V 1 5 3 = P 2 V 1 8 5 3 ⇒ P 1 V 1 5 3 = P 2   V 1 5 3 32 ⇒ P 2 = 32 P 1