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(NONE) The first law of thermodynamics is given by $\Delta U = q + w$.$1$. For an isochoric process,volume is constant,so $w = 0$,which implies $\Delt

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Adiabatic process: $\Delta U = w$

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(NONE) The first law of thermodynamics is given by $\Delta U = q + w$.$1$. For an isochoric process,volume is constant,so $w = 0$,which implies $\Delta U = q$. This is correct.$2$. For an adiabatic process,$q = 0$,which implies $\Delta U = w$. This is correct.$3$. For a cyclic process,the internal energy change $\Delta U = 0$,which implies $q = -w$. This is correct.$4$. For an isothermal process of an ideal gas,$\Delta U = 0$ (since internal energy depends only on temperature),which implies $q = -w$. This is also correct.Note: All given options are actually correct representations of the first law of thermodynamics for the specified processes. However,if the question implies a standard convention where $w = -P_{ext}\Delta V$,then all statements are valid.

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)

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