Calculate the change in enthalpy as 1kg of nitrogen is heated from 1000K to 1500K, assuming the nitrogen is an ideal gas at a constant pressure. The tempreature dependent specific heat of nitrogen is Cp = 39.06 - 512.79T^1.5 + 1072.7T^2 - 820.4T^3 where Cp is in kJ/kg-mol and T is in K
Answer is 697.27 kJ
This is the first time i've ever encountered something like "Temperature Dependent Specific Heat"
So I know
H = m*C_p*(T2-T1); Cp = 39.06 - 512.79T^1.5 + 1072.7T^2 - 820.4T^3
So I try to make something like C_p1:
C_p1 = 39.06 - 512.79T^1.5 + 1072.7T^2 - 820.4T^3; where T = 1000 C_p1 = -8.1934*10^11 C_p2 = 39.06 - 512.79T^1.5 + 1072.7T^2 - 820.4T^3; where T = 1500 C_p2 = -2.766466215*10^12 Cp2 - Cp1 = -3.8585 * 10^12
So yeah... Its not looking too good. Am i missing a formula?
The function looks like its easy to differentiate or integrate. Should I be doing something involving calculus?