If one mole of monoatomic gas \(\left(\gamma=\frac{5}{3}\right)\) is mixed with one mole of diatomic gas \(\left(\gamma=\frac{7}{5}\right)\), the value of y for the mixture is

Calculation:
If one mole of monoatomic gas (γ = 5/3) is mixed with one mole of diatomic gas (γ = 7/5), the value of γ for the mixture can be determined using the formula:

For the mixture of two gases, the effective γ (γ_mix) is given by:

γ_mix = (γ₁ × n₁ + γ₂ × n₂) / (n₁ + n₂)

Where:

• γ₁ = γ for monoatomic gas = 5/3
• γ₂ = γ for diatomic gas = 7/5
• n₁ = number of moles of monoatomic gas = 1
• n₂ = number of moles of diatomic gas = 1

Now substituting the values:

γ_mix = (5/3 × 1 + 7/5 × 1) / (1 + 1)

γ_mix = (5/3 + 7/5) / 2

γ_mix = (25/15 + 21/15) / 2

γ_mix = (46/15) / 2

γ_mix = 46/30 = 1.53

Therefore, the value of γ for the mixture is 1.53.

Correct Answer: Option 3 - 1.53