Aballoon contains 2.3 mol of helium at 1.0 atm , initially at 240 ∘c. what's the initial volume? what's the volume after the gas cools at constant pressure to 14 ∘c? how much work does the gas do in this process?

A) initial volume
We can calculate the initial volume of the gas by using the ideal gas law:

where
is the initial pressure of the gas
is the initial volume of the gas
is the number of moles
is the gas constant
is the initial temperature of the gas

By re-arranging this equation, we can find :


2) Now the gas cools down to a temperature of

while the pressure is kept constant: , so we can use again the ideal gas law to find the new volume of the gas


3) In a process at constant pressure, the work done by the gas is equal to the product between the pressure and the difference of volume:

by using the data we found at point 1) and 2), we find

where the negative sign means the work is done by the surrounding on the gas.

The answer is going to be c