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In common questions on thermodynamic processes, say for example a simple straight-forward question like "A gas at $T_1\ K$ and $P_1$ atm is suddenly released at atmospheric pressure. Find the final temperature of the gas", we assume the process to be adiabatic since no heat is exchanged between the system and the surroundings in that small interval of time. So my question is, do all quick processes have to be adiabatic, and similarly, is a slow process always isothermal?

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    $\begingroup$ No, a process can be so fast it can be a nonequilibrium process, which is not adiabatic. But most of the time in high school exams, 'fast' means adibatic. $\endgroup$ – knzhou Apr 3 '18 at 22:36
  • $\begingroup$ Is a slow process always isothermal? $\endgroup$ – M. S. L Apr 3 '18 at 23:20
  • $\begingroup$ It really depends, again. If there’s “ideal” insulation, then no. Or if you have some weird setup, like a gas slowly expanding inside a container inside an oven that slowly is heating up. But for an exam it’ll probably be isothermal unless they’re trying to be tricky. $\endgroup$ – knzhou Apr 3 '18 at 23:22
  • $\begingroup$ Could you give an example of the first bit? $\endgroup$ – M. S. L Apr 3 '18 at 23:26
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    $\begingroup$ A slow process doesn't have to be isothermal. For example, if you heat a gas in a closed container, its temperature will rise. If we expand a gas, adding a greater amount of heat to it than is necessary to hold its temperature constant, its temperature will rise. There are a zillion other examples. $\endgroup$ – Chet Miller Apr 3 '18 at 23:26
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If a process is rapid enough that there is little heat transfer between system and surroundings then treating it as adiabatic serves as a good first approximation (an adiabatic process strictly requires zero heat transfer). For example this approximation is employed in calculating sound speed through a medium, because contraction-expansion cycle of the medium due to passage of acoustic wave is considered rapid. Ultimately whether such an approximation is good enough is verified only by doing experiments.

A slow process on the other hand approximates a quasistatic process. A quasistatic process is one in which the system passes through a succession of equilibrium states while executing a process. A quasistatic process can be isothermal if the process involves maintaining constant temperature, but is not limited to it.

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Adiabatic means “without heat”. You can have quick processes either with (gas combustion) or without (Joule expansion) heat transfer.

Isothermal means “same temperature”. You can have slow processed that preserve temperature (ice melting in water; slow expansion while connected to a heat reservoir) or don’t (adiabatic expansion i.e. of rising air)

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