Temperatue and Presssure after volume change

In summary, the conversation discusses a sealed syringe with known pressure, temperature, and volume, and the effects on these variables when the volume is increased. The ideal gas law is mentioned and it is noted that one more equation is needed to find the pressure and temperature at the new volume. The polytropic process is also mentioned, with a specific polytropic index for air. Solutions for an isentropic process can be found on the Wikipedia page for isentropic processes.
  • #1
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I have a sealed syringe with air at known pressure P1, temperature T1 and volume V1. at some time I increase the volume of the syringe to V2, what will be the temperature T2 and pressure P2 at volume V2, right after the system reach to volume V2? The volume change process is relatively fast.

I know I can use the ideal gas law:

(P1*V1)/T1 = (P2*V2)/T2

But I'm still missing one more equation to find P2 and T2.

Any suggestions how it can be done? (It's a real life problem, I don't need a super accurate solution, estimated values are also good).
 
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  • #2
It is also a polytropic process, so:

P1 / P2 = (V2 / V1)n

Where n is the polytropic index, which is 1.4 for air if the process is isentropic (or one assume there is no heat transfer). You have all the relations derived for you on the isentropic process page of Wikipedia.
 

Related to Temperatue and Presssure after volume change

1. How does temperature affect pressure after a volume change?

According to the ideal gas law, when volume decreases and the number of moles of gas remains constant, an increase in temperature will result in an increase in pressure. This is because the increased temperature leads to an increase in the average kinetic energy of the gas molecules, causing them to collide more frequently and with greater force against the walls of the container, resulting in an increase in pressure.

2. Can pressure change without a change in temperature after a volume change?

Yes, pressure can change without a change in temperature after a volume change. This is known as Boyle's Law, which states that at a constant temperature, the pressure of a gas is inversely proportional to its volume. In other words, as volume decreases, pressure increases and vice versa.

3. How does a change in volume affect temperature and pressure?

A change in volume can affect both temperature and pressure. When volume decreases, temperature and pressure will increase. This is due to the direct relationship between temperature and pressure, as well as the indirect relationship between volume and pressure.

4. What is the relationship between temperature, pressure, and volume?

The relationship between temperature, pressure, and volume is described by the ideal gas law, which states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles of gas. In other words, as one variable increases, another variable will also increase, while the remaining variable will decrease.

5. How does changing the number of moles of gas affect temperature and pressure after a volume change?

If the volume of a gas is kept constant and the number of moles is increased, the temperature and pressure will also increase. This is because the increased number of gas molecules will result in more frequent and forceful collisions, leading to an increase in temperature and pressure. However, if the number of moles is decreased, the opposite will occur, with temperature and pressure decreasing.

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