A Carnot engine s operating between temperature T1 and T2 and has the efficiency of 1/6 .When thetemperature T2 is lowered by 53Kit efficiency becomes 1/4. Find temperatures T1 and T2.

Question

A Carnot engine is operating between temperature T1 and T2 and has the efficiency of 1/6 .When the temperature T2 is lowered by 53K it efficiency becomes 1/4. Find temperatures T1 and T2.

Answer 1

Looks like you will have a system of equations on your hand here, and this will of course involve the equation for efficiency of a Carnot engine, given as:

ε = (T_H - T_C)/ T_H

1) Write the first equation for the efficiency of 1/6. You can't sub in anything other than efficiency at this point.

2) Solve this equation for either T_H or T_C in terms of the other. The algebra should make it clear that T_H > T_C

3) Write a second equation for the efficiency of 1/4. Plug in (T_C - 53) for T_C, and substitute your expression from step 2. This should leave you a simple algebraic equation with just one variable. I get a T_C above 500K and of course T_H is higher than that.

Hope this helps,

Chris