Problem $1$

A Carnot heat engine receives heat from a high$-$temperature reservoir at $\backslash (527^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The heat rejected from this engine is supplied to a second Carnot engine. This second engine rejects heat to a low$-$temperature reservoir at $\backslash (17^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The first engine rejects $400$ kJ to the second engine. If both engines have the same efficiency, determine the following:

a$)$ The temperature of the high$-$temperature reservoir for the second engine or the temperature of the low$-$temperature reservoir of the first engine.

b$)$ The efficiency of each engine.

c$)$ The energy received by the first engine from the $\backslash (527^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ source.

d$)$ The work done by each engine.

Solution: