Question

For nitrogen gas the values of Cv and Cp at 25°C are 20.8 J K−1 mol−1 and 29.1 J K−1 mol−1, respectively. When a sample of nitrogen is heated at constant pressure, what fraction of the energy is used to increase the internal energy of the gas? How is the remainder of the energy used? The remainder of the energy is used to the volume of the gas against the constant pressure. How much energy is required to raise the temperature of 138.2 g N2 from 25.0°C to 86.0°C in a vessel having a constant volume? kJ

Answer 1

Answer:

71.4% of the energy is used to increase the internal heat of the gas, the remainder energy is used as work to increase the volume of the gas.  

Having a constant volume, the energy required to raise the temperature of the gas from 25° to 86° is 1729.77 KJ.

Explanation:

When a sample of Nitrogen, or any gas, is heated at constant pressure the gas expands and increases its volume, this requires energy that is called work.

Cv represents the value of the energy required to change the intern energy and Cp the work.

Cv/Cp = Energy used to increase the internal heat

$\frac{20.8}{29.1}=0.714$

The remainder of the energy is used as work to increase the volume of the gas.

At constant volume, all the energy is used to increase the internal energy of the gas. The energy is described with the equation, where n is the number of moles and in this case, Nitrogen has a molar mass of 28.02g/mol:

$\Delta E=nC_v\Delta T$

$\Delta E=(\frac{38.2g}{28.02g/mol})(20.8)(86-25)=1729.77 KJ$