Calculate the difference between C_ p and C_ V for 10 moles of an ideal gas

Step-by-step solution

For an ideal gas, the relationship between molar heat capacities at constant pressure C_ p,m and constant volume C_ V,m is given by Mayer's relation: C_ p,m - C_ V,m = R , where R is the universal gas constant. For n moles of an ideal gas, the total heat capacities are C_ p = n C_ p,m and C_ V = n C_ V,m . Therefore, the difference is C_ p - C_ V = n(C_ p,m - C_ V,m ) = nR . Given n = 10 moles and R = 8.314 J/(mol K), the difference is: C_ p - C_ V = 10 8.314 J/K = 83.14 J/K. Answer: 83.14 J/K