Question

The pressure P₁ and density d₁ of diatomic gas `(ϒ = 7/5)` changes suddenly to P₂(> P₁) and d₂ respectively during an adiabatic process. The temperature of the gas increases and becomes ______ times of its initial temperature.

`("given"  d_2/d_1 = 32)`

विकल्प

• `1/2`

• `3/2`

• `1/3`

• `1/4`

Answer 1

The pressure P₁ and density d₁ of diatomic gas `(ϒ = 7/5)` changes suddenly to P₂(> P₁) and d₂ respectively during an adiabatic process. The temperature of the gas increases and becomes `underlinebb(1/4)` times of its initial temperature.

Explanation:

For adiabatic process, PV^ϒ = constant

⇒ `P(m/d)^ϒ` = constant `[∵ d = m/V]`

⇒ `P/(d^ϒ)` = constant

⇒ `P_1/P_2 = (d_1/d_2)^ϒ = (1/32)^{7"/"5} = 1/128` `[∵ d_2/d_1 = 32]`

as PV = nRT ⇒ T ∝ PV ⇒ `T_1/T_2 = (P_1V_1)/(P_2V_2) = 1/128 32 = 1/4`