Adiabatic compression of gas at two temperatures

In summary, the conversation is discussing a system with a piston and displacer, where the pressure is equal to the sum of two masses divided by their respective volumes and temperatures. The question is how to modify this to account for temperature rise caused by adiabatic compression, and the solution involves writing the temperatures as functions of compression and considering equal pressures and varying temperatures during compression.
  • #1
Kalus
37
0
I have a system that looks like this:

zKjqb.jpg


The top part is a piston, whereas the bottom is a displacer.

I have looked at the Isothermal case for this system in a separate thread (https://www.physicsforums.com/showthread.php?t=553165)

But in short, the result was that the pressure of the system is equal to:

[tex]m=m_{gc}+m_{gh}[/tex]
[tex]P=\frac{mR}{V_{gc}/T_c +V_{gh}/T_h}[/tex]

How can I modify this to take into account the temperature rise caused by adiabatic compression? I suppose I need to write the T_gc + T_gh as functions of the compression by the top piston, but how?
 
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  • #2
Even if, as described in the linked thread, it is possible for the two chambers to exchange mass during compression (through a small gap surrounding the lower piston, so that the pressures are equalized at all times), when the system as described is compressed adiabatically, such exchange will not happen. Instead, both gas chambers will be compress by the same volume ratio at the overall volume:
$$\frac{V_c}{V_{c0}}=\frac{V_h}{V_{h0}}=\frac{V}{V_0}$$
Furthermore, the pressures in the two chambers will remain equal during the compression, and will vary as:
$$\frac{P}{P_0}=\left(\frac{V_0}{V}\right)^{\gamma}$$And the temperatues in the two chambers will vary as $$\frac{T_c}{T_{c0}}=\frac{T_h}{T_{h0}}=\left(\frac{V_0}{V}\right)^{\gamma-1}$$
 

1. What is adiabatic compression of gas at two temperatures?

Adiabatic compression of gas at two temperatures is a process in which a gas is compressed from one temperature to another without any heat exchange with the surroundings. This means that the process is reversible and no energy is lost or gained as heat.

2. How does adiabatic compression of gas at two temperatures differ from isothermal compression?

The main difference between adiabatic compression and isothermal compression is that in adiabatic compression, there is no heat exchange with the surroundings, while in isothermal compression, the temperature of the gas is kept constant by allowing heat to be exchanged with the surroundings.

3. What is the ideal gas law and how does it relate to adiabatic compression of gas at two temperatures?

The ideal gas law states that the pressure, volume, and temperature of an ideal gas are related by the equation PV=nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. This law is applicable to adiabatic compression of gas at two temperatures as it describes the relationship between these variables during the process.

4. What factors affect the adiabatic compression of gas at two temperatures?

The main factors that affect adiabatic compression of gas at two temperatures are the initial and final temperatures of the gas, the volume of the gas, and the type of gas being compressed. Additionally, the process must be carried out quickly to minimize heat exchange with the surroundings.

5. What are some real-world applications of adiabatic compression of gas at two temperatures?

Some common applications of adiabatic compression of gas at two temperatures include in refrigeration and air conditioning systems, gas turbines, and internal combustion engines. In these systems, the process is used to compress gas and increase its temperature, which can then be used to do work or cool a space.

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