One mole of ideal monoatomic gas (γ = 5/3) is mixed with two mole of diatomic gas (γ = 7/5). What is γ for mixture?
Correct answer: C. 19/13
- A. 3/2
- B. 23/15
- C. 19/13
- D. 4/3
Explanation
To find the effective gamma (γ) for the mixture, use the formula for the mixture of gases: γmix = (n1γ1 + n2γ2) / (n1 + n2), where n1 and n2 are the moles of each gas, and γ1 and γ2 are their respective gamma values. For this problem, n1 = 1 mole (monoatomic), γ1 = 5/3; n2 = 2 moles (diatomic), γ2 = 7/5. Therefore, γmix = (1*5/3 + 2*7/5) / (1+2) = (5/3 + 14/5) / 3 = 19/13. Hence, the correct answer is 19/13. The other options are incorrect because they either represent the gamma values of individual gases or miscalculate the mixture's gamma.
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About Molar Specific Heat of a Gas
Molar specific heat is the heat required to raise the temperature of one mole of a gas by one kelvin, expressed through Q = nCΔT. Questions compare the constant volume value Cv with the constant pressure value Cp, apply the ideal gas relation Cp − Cv = R, and identify how the thermodynamic process affects heat capacity.
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