# Thermodynamics - vessel with gas is filled with more gas

• frozen7
Additional air is pumped in, causing both pressure and temperature to rise. The mass of air can be found by using the ideal gas law. The final pressure and temperature can be used to find the quantity of air, and then the final pressure can be calculated after the vessel is cooled back to its initial temperature. In summary, by applying the ideal gas law and considering the changes in pressure and temperature, the mass of air, quantity of air, and final pressure can be determined.

## Homework Statement

A vessel of capacity 3m^3 contains air at a pressure of 1.5 bar and a temperature of 25 celcius. Additional air is now pumped into the system until the pressure rises to 30 bar and temperature rises to 60 celcius. Determine the mass of air and express the quantity as a volume at a pressure of 1.02 bar and a temperature of 20 celcius. If the vessel is allowed to cooled until the temperature is again 25 celcius, calculate the pressure in the vessel.

## The Attempt at a Solution

I do not really know how to start to solve this question. Thanks in advance to those who can help me. Does the additional air pumped in considered as the heat pumped in? Furthermore, should I consider whether the system is closed or opened firstly?

There are many levels at which this problem could be taken, and to work out which more context would be required (eg, super-compressibility any one?), but in simple terms it looks like PV=NRT is the equation required. One way of putting it is that (PV)/(NT) is constant, knowing this you can work out the impact on the fourth component of changing the other 3 of the components.

Remember that temperature above is absolute, not celcius.

You need to apply the equation a couple of times, and combine what you learned from the two applications.

frozen7 said:

## Homework Statement

A vessel of capacity 3m^3 contains air at a pressure of 1.5 bar and a temperature of 25 celcius. Additional air is now pumped into the system until the pressure rises to 30 bar and temperature rises to 60 celcius. Determine the mass of air and express the quantity as a volume at a pressure of 1.02 bar and a temperature of 20 celcius. If the vessel is allowed to cooled until the temperature is again 25 celcius, calculate the pressure in the vessel.
Figure out the number of moles of air initially. This follows simply from the ideal gas law: PV=nRT. You know P, V and T, so you can get n.

The second part is the same thing: find n, (where the total number of moles is the sum of the original plus the added air).

The third part, you know n now so you just find P from n, V, T.

AM