Question

Using Energy Concepts and the Ideal Gas Model

Argon contained in a closed, rigid tank, initially at 50°C, 2 bar, and a volume of 2 m3, is heated to a final pressure of 8 bar. Assuming the ideal gas model with k = 1.67 for the argon, determine the final temperature, in °C, and the heat transfer, in kJ.

Answer 1

Given data:

Tank volume,

Initial temperature,

Initial pressure,

Final pressure,

The ideal gas model is applied to argon with

To find the final temperature, apply the ideal gas law for Argon:

Here, and

In order to find the final temperature, however, we must first evaluate mass m using values from state 1.

From the Atomic or Molecular Weights of Selected Elements and Compounds table,

The molar mass of Argon

Therefore mass of argon,

Solving for temperature at state 2 and substituting values, we have

Therefore the final temperature,

To solve for heat transfer, we do an energy balance:

Here, because this is a closed, rigid tank with no means of heat transfer by work,

and kinetic and potential energy effects are ignored. Therefore, we must solve for specific internal energy.

For an ideal gas at constant volume,

And

Substituting into the equation for specific heat knowingand for argon,

Therefore the specific volume for argon at this state,

Collecting results and substituting into the energy balance to solve for heat transfer:

Therefore the heat transfer,