Question

Two moles of nitrogen gas at 25°C, confined within a cylinder by a piston maintaining a constant pressure of 1 atm, is heated with 5.30 kJ of energy. Assume all the energy is used to do work of expansion of the gas at 1 atm. What will be the final temperature of the gas? Recall ∆H = ∆E + P∆V and watch your units!

Answer 1

When we speak of a constant pressure process, it means that we are referring to an isobaric process.In this process the pressure and the force exerted are constant and the work done is given as PΔV. If you have a cylinder with a heavy piston and heat the gas in it, the gas expands due to increased energy. This is in accordance with Charles's law: the volume of a gas is proportional to its temperature.

First, by using the ideal gas equation I can calculate the volume under initial conditions

Tempertur change to K:

For future calculations, the volume in cubic meters will be needed, remembering that in 1 cubic meter there are cubic centimeters.

It's know that:

Theoretically, nitrogen has a Cp of 1,040Kj / Kg K. And the molecular weight is 28g / mol. The mass can be calculated using the following equation:

Then:

Since we do not know the value of T2, we reduce the equation as much as possible until we have:

Now, after expansion we will have new conditions since there will be a change in volume and temperature. Using the ideal gas equation again:

Substituting the values in the equation given by the first law of thermodynamics, Remembering that the pressure must be replaced in Kpa, knowing that 1atm = 101,325Kpa:

Grouping values: