Two moles of an ideal gas are compressed in a cylinder at a constant temperature of 80.0 ∘c until the original pressure has tripled. calculate the amount of work done by gas.

The work done by a gas during an isothermal process is given by:
(1)
where
n is the number of moles of the gas
R is the gas constant
T is the absolute temperature of the gas
is the ratio between the final volume and the initial volume of the gas

We need to calculate this ratio, and we can do it by using the gas pressure. In fact, for an isothermal process, Boyle's law states that the product between pressure and volume of the gas is constant:

which can be rewritten as

which is equivalent to

The problem says that the pressure of the gas is tripled, therefore the ratio between final and initial volume is:


Now we can use eq.(1) to calculate the work done by the gas. The absolute temperature is

The number of moles is n=2, therefore the work done is

And the work is negative, because it is done by the environment on the gas (the gas is compressed)

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