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## Homework Statement

The efficiency of a heat machine is ##E=\frac{Q_2-Q_1}{Q_2}## where Q

_{2}is the heat inserted because of the explosion and Q

_{1}is the heat that leaves through the exhaust.

It says in the book that E can be derived from the volumes ratio V

_{1}/V

_{2}:

$$E=1-\frac{1}{\left(V_1/V_2 \right)^{\gamma-1}}$$ why?

## Homework Equations

Adiabatic expansion: ##T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}##

## The Attempt at a Solution

$$E=1-\frac{1}{\left(V_1/V_2 \right)^{\gamma-1}}=\frac{T_2-T_1}{T_2}$$

But V

_{2}and T

_{2}have nothing to do with Q

_{2}, the heat from the explosion. also i don't know what's the connection between V

_{1}or T

_{1}and the heat lost through the exhaust.

I have just started studying the second law, maybe the book is excluding some explanations, it's an old book for high school but the level is quite high