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# Some equations are given below. Which of the following processes does not correctly represent the first law of thermodynamics ?

(a) Isothermal process : q = - w
(b) Cyclic process : q = - w
(c) Adiabatic process: $\Delta E$ = -w
(d) Expansion of a gas into vacuum : $\Delta E$ = q

Toolbox:
• The 1st Law of Thermodyamics simply states that energy can be neither created nor destroyed (conservation of energy). Thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than creation of energy from nothing.
• $\Delta$E = q + w (1st Law of Thermodynamics)
$\Delta$E = The change internal energy of the system,
q = The heat transferred into/out of the system,
w = The work done by/on the system.
This reformulation of the 1st Law tells us that once we define a system (remember we can define the system in any way that is convenient) the energy of the system will remain constant unless there heat added or taken away from the system, or some work takes place.
Answer: Adiabatic process: $\Delta E$ = -w
According to 1st Law of thermodynamics, $\Delta E = q + w$
For isothermal process, $\Delta$ E = 0, Hence, q = - w
For cyclic process, $\Delta$E = 0, Hence, q = - w
For adiabatic process, q = 0. Hence, $\Delta$E = w
For expansion in vaccum, w = 0. Hence $\Delta$E = q
$\therefore$ Adiabatic process: $\Delta E$ = -w is incorrect.