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`)

पर्याय

• `"P"/16`

• `"P"/8`

• `"P"/32`

• `"P"/64`

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:

`gamma = 5/3`

Case I: P₁ V₁ = P₂ V₂

P V = P₂ × 2 V

`therefore "P"_2 = "P"/2`

Case II:  `"P"_2 "V"_2^gamma = "P"_3"V"_3^gamma`

`("P"/2)("2V")^gamma = "P"_3 (16 "V")^gamma`

P₃ = `"P"/2 (2"V")^gamma/((16 "V")^gamma) = "P"/2 (1/8)^gamma`

`= "P"/2(1/2^3)^(5//3) = "P"/2(1/2)^5`

`= "P"/(2 xx 32) = "P"/64`