Question

(a) Consider the temperature dependent heat capacity of O2(g) given in the Resource
section of your textbook (29.355J/Kmol). What is the heat absorbed at constant pressure when 1 mole
of O2(g) is heated from 0o C to 500oC? (Hint: Integrate!)

(b) Construct a plot of Cp,m (for O2(g)) vs. T and plot it between 0 and 500
oC. What is the % error if you had used a temperature-independent heat capacity for part (a)?

Answer 1

a) Heat absorbed by oxygen will be given by:

Q = nCpdeltaT

In which Q is the heat absorbed, n is the number of moles, Cp is the heat capacity and delta T is the change in temperature.

In this case, as we'll use temperature dependent heat capacity and 1 mole, Q will be equal to CpdeltaT, which will be in the integral of the temperature dependent equation from 0 to 500 C.

Solving the integral, the result will be:

Q = 15,764.8 J

​b) ​*Plot was generated with Excel, using the heat capacity equation and intervals of 20 degree Celsius.

If we had used the temperature independent heat capacity, we would have obtained the following result:

Q = (500 - 0)C * 29.355J/Cmol = 14.677.5 J

Percent error would have been then:

%Error = (14,677.5 - 15,764.8) / 15,764.8 * 100 = 6.90%