Question

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)

• A. Adiabatic process: $\Delta U=-w$
• B. Isochoric process: $\Delta U=q$
• C. Cyclic process: $q=-w$
• D. Isothermal process: $q=-w$

Answer 1

The correct option is A Adiabatic process: $\Delta U=-w$

The first law of thermodynamics states that,
$\Delta U=q+w$
a) In an adibatic process $q=0$, so $\Delta U=w$.
b) In an isochoric process $\Delta V=0\Rightarrow W=P\Delta V=0$.
So, $\Delta U=q$
c) For a cyclic process $\Delta U=0$.
So, $q=-w$
d) For an isothermal process, $\Delta T=0\Rightarrow \Delta U=0$
Hence, $q=-w$