Question

A monoatomic gas of pressure p having volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is ____________.

`("ratio of specific heats" = 5/3)`

Options

• `"p"/8`

• `"p"/16`

• `"p"/64`

• `"p"/32`

Answer 1

A monoatomic gas of pressure p having volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is `underline("p"/64)`.

Explanation:

In Isothermal expansion,

p₁V₁ = p₂V₂

pV = p₂ (2V) = p₂ = `"p"/2`

In adiabatic expansion,

`"p"_2"V"_2^γ = "p"_3"V"_3^γ`

For monoatomic gas, γ = `5/3`

`"p"/2(2"V")^(5/3) = "p"_3(16"V")^(5/3)`

p₃ = `"p"/2 xx 1/8^(5/3) = "p"/(2 xx 2^5) = "p"/64`