Question

Which one of the following equations does not correctly represent the first law of thermodynamics for the given process?

• A. Isothermal process: $q=-w$
• B. Cyclic process: $q=-w$
• C. Isochoric process: $\Delta U=q$
• D. Adiabatic process: $\Delta U=-w$
• E. Expansion of gas into vacuum: $\Delta U=q$

Answer 1

Answer: (D)

Adiabatic process: $\Delta U=-w$

The first law of thermodynamics gives us the following equation :

$\Delta U=q+w$

$\Delta U=n{C}_V\Delta T$

$W=-P\Delta V$

For siothermal process :- $\Delta T=0\Rightarrow \Delta V=0$

$\therefore q=-W$

For cyclic process :- $\Delta U=0$ (as it is a state function)

$\therefore q=-w$

For isochoric process :- $\Delta V=0\Rightarrow W=0$

$\therefore \Delta U=q$

For adiabatic process :- $q=0$

$\therefore \Delta U=W$

For expansion of gas into vacuum :- $W=0$

$\therefore \Delta V=q$