5 moles of unknown gas is heated at constant volume from 10 , °C to 20 , °C . The molar specific heat of this gas at constant pressure c_p = 8 cal/mol.°C and R = 8.36 J/mol.°C. The change in the internal energy of the gas is _______ calorie.

Step-by-step solution

Given n = 5 moles, T = 20^ C - 10^ C = 10^ C . The molar specific heat at constant pressure is c_p = 8 cal/mol ^ C . The universal gas constant is R = 8.36 J/mol ^ C . Converting R into calories, we use 1 cal = 4.18 J : R = 8.36 4.18 cal/mol ^ C = 2 cal/mol ^ C Using Mayer's relation, the molar specific heat at constant volume is: c_v = c_p - R = 8 - 2 = 6 cal/mol ^ C The change in internal energy of the gas is given by: U = n c_v T U = 5 6 10 = 300 cal Answer: 300