Question

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

Options

• P

• 8P

• 32P

• 64P

Answer 1

A monoatomic gas at pressure P and volume V is suddenly compressed to one eights of its original volume. The final pressure at constant entropy will be 32P.

Explanation:

For monoatomtc gas, ϒ = `5/3`

For an adiabatic process, PV^ϒ = constant

For an adiabatic process, PV^ϒ = P'(V')^ϒ

⇒ PV^5/3 = P'`(V/8)^{5"/"3}` `("Given", V^'= V/8)`

⇒ P' = `(8)^{5"/"3}P = (2)^5P` = 32 P