A mixture consists of 1 mole of helium ( C_p = 2.5 R , C_V = 1.5 R ) and 1 mole of hydrogen ( C_p = 3.5 R , C_V = 2.5 R ). Determine the values of C_p , C_V , and for this mixture.

Step-by-step solution

For a mixture of gases, the molar heat capacity at constant volume is given by: C_V = n₁ C_ V1 + n₂ C_ V2 n₁ + n₂ Substituting the given values: C_V = 1 1.5 R + 1 2.5 R 1 + 1 = 4 R 2 = 2 R The molar heat capacity at constant pressure for the mixture is given by: C_p = n₁ C_ p1 + n₂ C_ p2 n₁ + n₂ Substituting the given values: C_p = 1 2.5 R + 1 3.5 R 1 + 1 = 6 R 2 = 3 R The ratio of specific heats for the mixture is: = C_p C_V = 3 R 2 R = 1.5