Propane gas (C3H8) behaves like an ideal gas with ? = 1.127. Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure.

Solution 26E Step 1 of 5: In the given problem, we need to calculate the heat capacities under two different conditions by using the ratio of the Molar specific heat capacities = 1.127. The Molar Specific heat capacity (C) of a substance is the amount of heat required the rize the temperature of a mole of substance by a degree. Molar Specific Heat capacity can be measured under conditions of constant pressure or constant volume. Thus, two distinct heat capacities can be defined: CP=Molar heat capacity at constant Pressure and C = Volar heat capacity at constant volume Step 2 of 5: The ratio of this heat capacities is constant for a particular substance and that constant is denoted by That is = C p………….1 CV Also we know that, the difference of molar heat capacities is equal to the universal gas constant, That is C P C =VR Where R is universal gas constant. Solving for heat capacity at constant pressure,PC = R + V ………….2 Step 3 of 5: Using C = R + C in equation 1, P V R+CV = CV = R + 1 C V Solving for C hVat capacity at constant volume in terms if gas constant and heat capacity ratio: , 1= R CV R C V 1 …………..3