The specific internal energy of formaldehyde (HCHO) vapor at 1 atm and moderate temperatures is given by the formula U(J/mol) = 25.96T + O.02134T² where T is in °C.

(a) Calculate the specific internal energies of formaldehyde vapor at 0°C and 100°C. What reference temperature was used to generate the given expression for U?

(b) The value of U calculated for 100°C is not the true value of the specific internal energy of formaldehyde vapor at this condition. Why not? 

(c) Use the closed system energy balance equation to calculate the heat (J) required to raise the temperature of 3.0 mol HCHO at constant volume from 0°C to 100°C. List all of your assumptions.

(d) From the definition of heat capacity at constant volume, derive a formula for C_v (T) [J/mol ∙ °C]. Then use this formula and Equation 8.3-6 to calculate the heat (J) required to raise the temperature of 3.0 mol of HCHO (v) at constant volume from 0°C to 100°C. [You should get the same result you got in part (c)]