# Do all adiabatic processes involve a change in temperature?

I learnt that adiabatic processes involve no heat exchange between the system and the environment. Does this mean that all adiabatic processes involve some changes in temperature then?

Thanks a lot!

• Yes... free expansion is an exception (its actually not right to call free expansion as an adiabatic process) – Yashas May 19 '16 at 4:59
• Adiabatic expansion does involve certain change in temperature; also, what's wrong about calling it adiabatic? Essentially, if we fix two variables in the equation of state, we are left without any degrees of freedom. Thus the answer is "yes", unless we have multiple components, in which case it turns to "no". Mixing of two gases at the same temperature can be an example of adiabatic processes without change in temperature. – Ivan Neretin May 19 '16 at 5:07
• I believe its physically impossible to have an adiabatic process by mixing two gases. – Yashas May 19 '16 at 5:19
• What's physically impossible about having two gases at the same temperature, and then gently mixing them? – Ivan Neretin May 19 '16 at 5:30
• Let's say I'll just open the valve between the two tanks. We don't really have to be gentle: it will be an adiabatic process anyway. – Ivan Neretin May 19 '16 at 7:34

The first law of thermodynamics says, $$\Delta U = Q - W$$

By definition, no heat is exchanged between the system and the surroundings in an adiabatic process. Therefore, the 1st law reduces to,

$$\Delta U = -W$$

In an adiabatic process, $PV^\gamma =const.$ has to be followed. If you change pressure, the above equation implies that volume changes. If the volume changes, there will be some work done which in turn will change the internal energy of the system. Therefore, the temperature changes.

You can also come to the same conclusion using ideal gas equation.

We know the ideal gas equation,

$$PV = nRT$$

If there should be no change in temperature, $PV$ should remain constant.

But in case of an adiabatic process, we know that $$PV^\gamma =constant$$

So if you change one of those parameters, the product $PV$ will obviously change (so as to keep $PV^\gamma$ constant). Hence, temperature always changes in an adiabatic process.

*I have ignored ridiculously insane cases where matter can exit/enter the system through an adiabatic wall (which isn't possible). If you could discover a wall that allows matter to move across and does not allow heat to conduct through it, you deserve a nobel prize.

*Free expansion and mixing gases are two processes where the process is adiabatic and there is no temperature change.