A mixture of ideal gases N2 and He are taken in the mass ratio of 14 : 1 respectively. Molar heat capacity of the mixture at constant pressure is:
Correct answer: D. 19R/6
- A. 6R/19
- B. 13R/6
- C. 6R/13
- D. 19R/6
Explanation
To find the molar heat capacity of the mixture at constant pressure (Cp), we use the formula for the molar heat capacity of a mixture:Cp,mix = (x1Cp1 + x2Cp2) / (x1 + x2)where x1 and x2 are the molar fractions of N2 and He respectively. The molar mass of N2 is 28 g/mol, and for He, it is 4 g/mol. Given the mass ratio of 14:1, their mole ratio is 1:7. Thus, the effective molar heat capacity is calculated as follows:Cp,mix = (1 * Cp,N2 + 7 * Cp,He) / 8 = 19R/6.Options A, B, and C are incorrect as they do not correctly reflect this calculation. They fail to appropriately account for the weightage of each gas's contribution to the total heat capacity based on their molar heat capacities and the proportions present in the mixture.
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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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