It says that in adiabatic process, the heat is constant but the temperature is not. My question is, if you increase the pressure, the temperature is going to rise as pV = kT. But we know that the energy, E = $\frac{3}{2}RT$
So if T is increased here, it must increase the Energy also. Where does the system get energy from? Does the increase of pressure contribute?
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$\begingroup$ Think about: how do you increase the pressure in a system? How do you decrease the volume? $\endgroup$– dannuicCommented Apr 18, 2016 at 20:06
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2 Answers
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To decrease the volume of the gas and hence increase its pressure work needs to be done. That is an external force must move through a distance.
The work done can be found by working out the integral $\int P \;dV$ which is the area under a Pressure, $P$, against volume, $V$, graph.
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Consider an adiabatic container with a partition. Let one side be filled with an ideal gas and the other side is filled with vacuum.Now, keeping the pressure on this system constant , I remove the partition thereby changing the volume which in turn changes the temperature of the system and the pressure.Using the adiabatic relationships between P,V,T, the exact magnitude of these changes can be calculated and relationships can be established between variables.If volume is decreased , the molecules come closer and hit the walls of the container thus increasing the pressure and the temperature. So , the energy of the molecules increases. Although not completely focusing on your question, you might find this article useful for an intuitive feel: https://www.quora.com/If-volume-and-temperature-are-directly-proportional-according-to-the-combined-gas-laws-then-why-does-a-gas-cool-a-decrease-in-temperature-as-it-expands-an-increase-in-volume
