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JEE Main 2018 · Physics · Thermodynamics and Kinetic Theory of Gases · medium

A rigid container holds 2 mol of helium and 1 mol of oxygen (treated as a rigid diatomic gas with no vibrational modes) in thermal equilibrium.

Single correct option

A rigid container holds 22 mol of helium and 11 mol of oxygen (treated as a rigid diatomic gas with no vibrational modes) in thermal equilibrium. The ratio Cp/CvC_p/C_v of the mixture is
  1. A. 75\dfrac{7}{5}
  2. B. 1511\dfrac{15}{11}
  3. C. 32\dfrac{3}{2}
  4. D. 2315\dfrac{23}{15}
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Answer: (B) 1511\dfrac{15}{11}

The heat capacities of components add per mole of each: Cvmix=2(32R)+1(52R)=112RC_v^{mix}=2\left(\tfrac32R\right)+1\left(\tfrac52R\right)=\tfrac{11}{2}R and Cpmix=2(52R)+1(72R)=152RC_p^{mix}=2\left(\tfrac52R\right)+1\left(\tfrac72R\right)=\tfrac{15}{2}R (both for the total 33 mol). Hence γ=15/211/2=1511≈1.36\gamma=\dfrac{15/2}{11/2}=\dfrac{15}{11}\approx1.36. Simply averaging the two γ\gamma values, 12(53+75)=2315\tfrac12\left(\tfrac53+\tfrac75\right)=\tfrac{23}{15}, is incorrect because the gases are not present in equal heat capacity.
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