Assume that for an ideal gas, within a temperature interval, the dependence of the isobaric specific heat on temperature can be approximated by a quadratic equation c_P - (T) = K₁ + K₂ T + K₃T², where K_1,2,3 are constants.

(a) Obtain the equation for u - (T) and h - (T).
(b) The coefficients for c_P - (T) of carbon dioxide in the range 100 – 1000 K are K₁ = 23.87, K₂ = 52.85 × 10⁻³ and K₃ = −23.47 × 10⁻⁶. Calculate the difference in internal energy and enthalpy of carbon dioxide between 340 K and 290 K at 0.1 MPa.