Question

Which of the following is not correct for an ideal gas as per the first law of thermodynamics?

• A. Adiabatic $∆U=-w$
• B. Isothermal $q=-w$
• C. cyclic $q=-w$
• D. Isochoric $∆U=q$

Answer 1

The correct option is A

Adiabatic $∆U=-w$

Explanation for the correct answer:

In case of option A.

1. The first law of thermodynamics may be given mathematically: $∆U=q+w$, where $∆U$= Change in internal energy, $q$=Heat supplied or rejected, $w$= Work done.
2. In case of adiabatic process, $q=0$. Thus $∆U=w$.
3. Hence, option A is the correct option.

Explanation for the incorrect answers:

In case of option B.

1. In the case of an isothermal process, the temperature remains constant.
2. In that case, the internal energy does not change.
3. So the first law becomes $q+w=0,q=-w$,
4. Thus, option B is the incorrect option.

In case of option C.

1. In a cyclic process, since the system returns to its initial state, the change in internal energy must be zero.
2. Therefore, by the first law of thermodynamics, the net heat given to the system must be equal to the net work done by the system. $q+w=0,q=-w$
3. Thus, option C is the incorrect option.

In case of option C.

1. For an isochoric process, volume remains unchanged.
2. Change in volume is directly proportional to work done. or $w=\int pdv,dv=0,w=0$
3. So, in this case, work done will be zero, and the first law becomes $∆U=q$

Hence, option A is the correct option.