Question

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

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

Answer 1

The correct option is D Expansion of a gas into vacuum : $\Delta$E = q

Isothermal Process :

Temperature is constant hence $△$ E = 0

From 1st law of thermodynamics $△$ E = q + w

Since$△$ E is 0, hence q = -w

Cyclic Process :

In cyclic process, change in all state functions are zero, so $△$ E being state function = 0

From 1st law of thermodynamics $△$ E = q + w

Since $△$ E is 0, hence q = -w

Adiabatic Process :

In adiabatic process q = 0

Hence from 1st law of thermodynamics $△$ E = w

In free expansion :

In free expansion $△T=0,q=0,w=0,△U=0$

Hence, option D is correct.