A System under goes a Cyclic Process in which it absorbs Q1 heat and gives out Q2 heat. The effi

step 1 Hello students and the question is given that a system undergoes a cyclic process in which it ab

A System under goes a Cyclic Process in which it absorbs Q1...

A System under goes a Cyclic Process in which it absorbs $\mathrm{Q}_{1}$ heat and gives out $\mathrm{Q}_{2}$ heat. The efficiency of the Process $\eta$ and the work done is $\mathrm{W}$. Which formula is wrong ? is (A) $\mathrm{W}=\mathrm{Q}_{1}-\mathrm{Q}_{2}$ (B) $\eta=\left(\mathrm{Q}_{2} / \mathrm{Q}_{1}\right)$ (C) $\eta=\left(\mathrm{W} / \mathrm{Q}_{1}\right)$ (D) $\eta=1-\left(\mathrm{Q}_{2} / \mathrm{Q}_{1}\right)$

A System under goes a Cyclic Process in which it absorbs $\mathrm{Q}_{1}$ heat and gives out $\mathrm{Q}_{2}$ heat. The efficiency of the Process
$\eta$ and the work done is $\mathrm{W}$. Which formula is wrong ? is
(A) $\mathrm{W}=\mathrm{Q}_{1}-\mathrm{Q}_{2}$
(B) $\eta=\left(\mathrm{Q}_{2} / \mathrm{Q}_{1}\right)$
(C) $\eta=\left(\mathrm{W} / \mathrm{Q}_{1}\right)$
(D) $\eta=1-\left(\mathrm{Q}_{2} / \mathrm{Q}_{1}\right)$

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Key Concepts

First Law of Thermodynamics

The first law of thermodynamics, or the law of energy conservation, states that the energy added to a system as heat minus the energy lost as work equals the change in the system's internal energy. In a cyclic process, since the internal energy returns to its initial value, the net work done is equal to the net heat added, establishing relationships such as W = Q_in - Q_out.

Thermal Efficiency

Thermal efficiency is a measure of how well a heat engine converts the input heat into useful work. It is defined as the ratio of the work output to the heat input (? = W/Q_in). Additionally, it can be expressed as ? = 1 - (Q_out/Q_in), reflecting the fact that some of the input heat must be expelled, which inherently limits the efficiency of the engine.

Cyclic Process

A cyclic process is one in which the system undergoes a series of changes and eventually returns to its original state. This concept is crucial in thermodynamics because it implies that the net change in internal energy over a complete cycle is zero, allowing the analysis of work and heat transfer solely based on their differences.

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