Question

One mole of ideal monoatomic gas ( γ = 5/3) is mixed with one mole of diatomic gas ( γ = 7/5) what is γ For the muxture ? γ denotes the ratio of specific heat at constant pressure, to that at constant volume ? [AIEEE 2004] ​

Answer 1

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Answer 2

Explanation:- mayer's formula is Cₚ- Cᵥ and γ = Cₚ/Cᵥ

Therefore , using above two relations , we find

Cᵥ = R/γ -1

For a mole of monatomic gas

γ = 5/3 ∴ Cᵥ = R/(5/3)-1 = 3/2R

For a moleba diatomic gas, γ = 7/5

∴ Cᵥ = R/(7/5)-1 = 5/2R

⟹ when , these two moles are mixed , then heat required to raise the temprature to 1°C is

Cᵥ = 3/2R+5/2R = 4R

Hence, for one mole , heat required = 4R/2 = 2R

∴ Cᵥ = 2R ⟹ R/γ-1 = 2R or γ = 3/2 Answer .

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Alternate method

• n₁+ n₂/γ-1 = n₁/γ₁ -1 + n₂/γ₂-1

• Here ,n₁ = 1 , n₂ = 1 γ ₁ = 5/3 and γ₂ = 7/5

• ∴ 1+1 /γ-1 = 1/(5/3)-1 + 1/(7/5)

• ⟹ 2/γ - 1 = 3/2+5/2 or 2/γ-1 = 8/2

• or 2/γ-1 = 4

• ⟹ γ = 2/4+1

• hence , γ = 3/2