Amole of ideal gas expands at t=27 °c. the pressure changes from 20 atm to 1 atm. what’s the work that the gas has done and what’s the heat absorbed by the gas?

Explanation:

We know that the differential work made by the gas  its defined as:

We can solve this by integration:

but, first, we need to find the dependence of Pressure with Volume. For this, we can use the ideal gas law

This give us

As n, R and T are constants

But the volume is:

Now, lets use the value from the problem.

The temperature its:

The ideal gas constant:

So:

We know that, for an ideal gas, the energy is:

where its the internal energy of the gas. As the temperature its constant, we know that the gas must have the energy is constant.

By the first law of thermodynamics, we know

where is the Work made by the gas (please, be careful with this sign convention, its not always the same.)

So:

the answer is 12 as i may remember

: )