Nitrogen gas has values of Cv and Cp of 20.8 and 29.1 J K-1 mol-1, respectively. When a certain amount of nitrogen is heated at constant pressure, what fraction of the heat Q is used to increase the internal energy of the gas, and how is the remaining energy used?

A) 3/2 of Q is used to increase internal energy, the rest used for work.
B) All of Q is used to increase the internal energy of the gas and there is no remaining energy.
C) ~ 0.7 (70%) of Q is used to increase the internal energy and the rest goes to pressure-volume work.
D) Most of Q is used up as work in the expansion of the gas at constant pressure.
E) 58% of Q does work, and the rest goes to increasing the internal energy of the gas.

Thermodynamics is not my field. I would go with C but get a second opinion.

I don't think A is right because for a diatomic gas Cp is 7/2R.
B. B can't be right because at constant P there will be pdV work.
C. The difference between Cv and Cp is 8.3 and that is about 28.5% of 29.1 so that much energy goes to work leaving about 71.5% for heat and that's close to 70%.
D. Doesn't sound reasonable
E. I tried various manipulations to get 58% and couldn't do it so I don't know how they arrived at this as a possible answer.
I would be interested in knowing the correct answer (and WHY of course) if it isn't C.

To determine the fraction of heat Q that is used to increase the internal energy of the gas, we need to understand the meaning of Cv and Cp.

Cv is the molar heat capacity at constant volume, which represents the amount of heat required to increase the temperature of one mole of gas by 1 Kelvin at constant volume.

Cp, on the other hand, is the molar heat capacity at constant pressure, which represents the amount of heat required to increase the temperature of one mole of gas by 1 Kelvin at constant pressure.

The difference between Cp and Cv is given by the equation Cp - Cv = R, where R is the gas constant.

In this case, the values are given for nitrogen gas as Cv = 20.8 J K-1 mol-1 and Cp = 29.1 J K-1 mol-1.

When a certain amount of nitrogen gas is heated at constant pressure, it means that we are applying heat while keeping the pressure constant. In this scenario, the remaining energy is used for work.

To determine which fraction of Q is used to increase the internal energy and how the remaining energy is used, we need to compare Cv and Cp.

If Cv and Cp were equal, then all of the heat would be used to increase the internal energy, and there would be no remaining energy for work. However, in this case, Cv is smaller than Cp, indicating that more heat is required to increase the temperature at constant pressure. This indicates that some of the heat is used for work.

So, to find the fraction of Q used to increase the internal energy, we can divide the difference between Cp and Cv by Cp.

Fraction of Q used to increase internal energy = (Cp - Cv) / Cp

Fraction of Q used to increase internal energy = (29.1 - 20.8) / 29.1

Fraction of Q used to increase internal energy ≈ 0.715 (approximately)

Therefore, the correct answer is option C) ~ 0.7 (70%) of Q is used to increase the internal energy and the rest goes to pressure-volume work.