Answer to Question #193536 in Molecular Physics | Thermodynamics for Mr Okay Okay

Question

An ice-making machine operates in a Carnot cycle. It takes heat from water at 0.0°C and rejects heat to

a room at 24.0°C. Suppose that 85.0 kg of water at 0.0_C are converted to ice at 0.0°C. (a) How much

heat is discharged into the room? (b) How much energy must be supplied to the device?

Answer 1

answer:-

a)

Q_C = heat from ice , Q_H heat discards to the room

L_f= heat fusion =$334\times 10^3 J/kg$

$Q_c=mL_f=85kg\times334\times 10^3 J/kg=1.84\times10^4kJ$

now

$\frac{Q_C}{Q_H}=-\frac{T_C}{T_H}\\ {Q_C}=-{Q_H}\frac{T_C}{T_H}=-(2.84\times10^4kJ)(\frac{297K}{273K})\\ Q_c=\boxed{-3.09\times10^4kJ}$

the negative sign is due to discarding the heat to the hot reservoir

b)

$|Q_H|=Q_c+|W| \\ |W|=Q_C-|Q_H|=2.84\times10^4-3.09\times10^3kJ\\ W=-2.50\times10^3kJ$