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An isothermal change is when the temperature remains constant... but how is it able to exchange heat with its surroundings without the temperature rising or lowering? Would isothermal changes always be apart of an isolated system then?
With an isothermal process, the heat is equal to the opposite of the work value, remember the equation ∆U=q+w. The first law of thermodynamics, relating to the law of conservation of matter and energy explains why when a process is isothermal ∆U=0, q=-w. As long as you are capable of calculating the work, you can find the heat of the system.
Remember heat does not equal temperature. Isothermal means temperature is held constant, but heat is not restricted. As a result, deltaU equals 0. When we plug this into the first law of thermodynamics equation of deltaU=q+w, we get q=-w.
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