Question

Assertion: Equal volumes of monatomic and polyatomic gases are adiabatically compressed separately to equal compression ratio `("P"_2/"P"_1)`. Then monatomic gas will have greater final volume.

Reason: Among ideal gases, molecules of a monatomic gas have the smallest number of degrees of freedom.

Options

• Assertion is true, Reason is true and Reason is correct explanation for Assertion.

• Assertion is true, Reason is true but Reason is not a correct explanation for Assertion.

• Assertion is true, Reason is false.

• Assertion is false, Reason is true.

Answer 1

Assertion is false, Reason is true.

Explanation:

`"P"_1^gamma "V"_1^gamma = "P"_1 "V"_2^gamma`

`therefore ("P"_2/"P"_1) = ("V"_1/"V"_2)^gamma`

`therefore "V"_2 = "V"_1 ["P"_1/"P"_2]^(1/gamma') = "V"_1 "C"^(1//gamma)`    ....(C > 1)

`therefore "V'"_2 = "V'"_1 ["P"_1/"P"_2]^(1/gamma') = "V"_1 "C"^(1//gamma)`

`because gamma > gamma' [(ϒ -> "Monatomic"),(ϒ"'" -> "Polyatomic")] Rightarrow "V'"_2 > "V"_2`

This means, Assertion is false, Reason is true.