A mathematical statement of the First Law of Thermodynamics is U = q + w . This

Question

A mathematical statement of the First Law of Thermodynamics isU = q + w. This holds for allprocesses.
Assume that the only type of work done is pV-work. Showthat U = 0 for a process in an isolated system. Showthat U = q for a process that occurs atconstant volume. Show that H = 0 for an adiabaticprocess at constant pressure.

Explanation / Answer

isolated system no heat exchange and no change in volume q = 0; w = 0 => U = 0 constant volume w = integral [P*dV]        if constant volume, dV = 0   => w = 0 U = q + w = q + 0 = q adiabatic process at constant pressure H = U + PV = H = q + integral [V*dP] if dP = 0 (constant pressure), then the integral is 0 If adiabatic q = 0 Thus H = 0

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