Question

A piston-cylinder assembly contains 2 lb of air at a temperature of 540 degrees R and a pressure of 1 atm. The air is compressed to a state where the temperature is 840 degrees R and the pressure is 6 atm. During the compression there is a heat transfer from the air to the surroundings equal to 20 Btu. Determine the work during the process, in Btu. State your assumptions, if any.

Answer 1

Answer:

$W=-123.8Btu$

Explanation:

Hello,

In this problem, the piston-cylinder assembly make us state the energy balance as:

$Q-W=\Delta U$

Thus, we must now compute $\Delta U$ in terms of Cv as follows:

$\Delta U=mCv(T_2-T_1)\\\Delta U=2lb*0.173\frac{Btu}{lb*R}*(840R-540R)\\ \Delta U=103.8Btu$

Now, since heat is given off, its sign is negative, thus, the work is computed as:

$W=Q-\Delta U\\W=-20Btu-103.8Btu=-123.8Btu$

This work means that work was done over the system in order to allow the compression.

The suppositions were:

- The change in the internal energy is a function of the temperature.

- Air is an ideal gas.

Best regards.