If two moles of diatomic gas and one mole of mono atomic gas are mixed then the ratio of specific heats is:
Correct answer: C. 19/13
- A. 7/3
- B. 5/4
- C. 19/13
- D. 15/19
Explanation
The ratio of specific heats, γ, is given by the formula γ = Cp/Cv. For a mixture of gases, this is calculated using:γ = (n1Cp1 + n2Cp2 + ...)/(n1Cv1 + n2Cv2 + ...)For diatomic gases, Cp = 7R/2 and Cv = 5R/2. For monoatomic gases, Cp = 5R/2 and Cv = 3R/2.In this question, we have two moles of diatomic gas and one mole of monoatomic gas. Plugging in the values:γ = [(2 * 7R/2) + (1 * 5R/2)] / [(2 * 5R/2) + (1 * 3R/2)]This simplifies to γ = 19/13, making Option C correct. Other options are incorrect as they arise from miscalculations.
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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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