The ideal gas heat capacity of nitrogen varies with temperature. It is given by:
Cp = 29.42 - (2.170*10^-3 ) T + (0.0582*10^-5 ) T2 + (1.305*10^-8 ) T3 – (0.823*10^-11) T4
T in K and Cp in Joule/(mole-K). Assuming that N2 is an ideal gas:
A) How much internal energy (per mole) must be added to nitrogen to increase its temperature from 450 to 500 K. B) Repeat part A for an initial temperature of 273 K and final temperature of 1073 K.

A)  1059 J/mol

B)  17,920 J/mol

Explanation:

Given that:

Cp = 29.42 - (2.170*10^-3 ) T + (0.0582*10^-5 ) T2 + (1.305*10^-8 ) T3 – (0.823*10^-11) T4

R (constant) = 8.314

We know that:

We can determine from above if we make the subject of the formula as:

A).

The formula for calculating change in internal energy is given as:

If we integrate above data into the equation; it implies that:

Hence, the internal energy that must be added to nitrogen in order to increase its temperature from 450 to 500 K = 1059 J/mol.

B).

If we repeat part A for an initial temperature of 273 K and final temperature of 1073 K.

then T = 273 K & T2 = 1073 K

∴

the answer your looking for is c).