Question

Could you have a heat engine with $\eta >1$? Explain.

Short answer

A heat engine with$n>1$is No.

Step-by-step solution

Step :1 Introduction 

A heat engine is a machine that turns heat into mechanical energy. It receives heat from a reservoir, then performs some work, such as moving a piston or raising a weight, before releasing heat energy into the sink.

Step ;2 Explanation 

Let us derive an expression for the efficiency of a heat engine. We can define heat engine efficiency as:

$\begin{array}{r}\eta \end{array}$$=W{Q}_1$

W

= Work done by the engine

$Q_1$

= Heat taken from the source

Step :3 Substitution 

$\text{Since}\eta =W_{\text{out}}/Q_{\text{in}}\text{and}{W}_{\text{out}}<Q_{\text{in}}\text{always, hence}\eta <1\text{always.}$

No