Thermodynamics - vessel with gas is filled with more gas

In summary: 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.
  • #1
frozen7
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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.

Homework Equations



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?
 
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  • #2
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.
 
  • #3
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
 

1. How does the amount of gas in a vessel affect its thermodynamic properties?

The amount of gas in a vessel plays a crucial role in determining its thermodynamic properties. The more gas present in the vessel, the higher the pressure and temperature will be, as well as the overall energy and entropy of the system. This is due to the increased number of gas molecules colliding with each other and the walls of the vessel, leading to a greater amount of energy being transferred and an increase in disorder within the system.

2. Can the amount of gas in a vessel be changed without affecting its thermodynamic properties?

No, the amount of gas in a vessel directly affects its thermodynamic properties and cannot be changed without altering these properties. Adding or removing gas from a vessel will result in changes to its pressure, temperature, energy, and entropy, as well as any other thermodynamic variables. These changes are a direct result of the gas molecules interacting with each other and the walls of the vessel.

3. How does the ideal gas law apply to a vessel with more gas?

The ideal gas law, which states that the pressure, volume, and temperature of a gas are directly proportional, applies to a vessel with more gas in the same way it applies to any other gas system. However, the increased amount of gas in the vessel will lead to a higher pressure and temperature, as well as a larger volume in order to maintain a constant ratio between these variables.

4. What is the relationship between the amount of gas in a vessel and its internal energy?

The amount of gas in a vessel directly affects its internal energy, as the energy of a gas system is dependent on the number of gas molecules present. An increase in the amount of gas will lead to an increase in the internal energy of the system, as there are more molecules available to transfer and store energy. Likewise, a decrease in the amount of gas will result in a decrease in the internal energy of the system.

5. Can the amount of gas in a vessel ever reach an equilibrium state?

Yes, the amount of gas in a vessel can reach an equilibrium state, where the pressure, temperature, and other thermodynamic properties of the gas remain constant over time. This occurs when the rate of gas molecules entering and leaving the vessel is equal, resulting in a balance between the energy and entropy of the system. However, this state is often only temporary and can be disrupted by changes in external factors, such as temperature or pressure.

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Thank you for your response AM. I appreciate it and will work through the steps.
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