Question

A food product is being frozen in a system capable of removing 6000 kJ of thermal energy. The product has a specifi c heat of 4 kJ/(kg C) above the freezing temperature of 2 C, the latent heat of fusion equals 275 kJ/kg, and the frozen product has a specifi c heat of 2.5 kJ/(kg C) below 2 C. If 10 kg of product enters the system at 10C, determine the exit temperature of the product..

Answer 1

Answer : The exit temperature of the product is, $-35.2^oC$

Explanation :

Total heat = Heat lost by liquid + Latent heat of fusion + Heat lost by frozen

$Q=m\times c_1\times (T_2-T_1)+m\times L_f+m\times c_2\times (T_4-T_3)$

where,

Q =  Total heat = 6000 kJ

m = mass of product = 15 kg

$c_1$ = specific heat of liquid = $4kJ/kg^oC$

$L_f$ = latent heat of fusion = $275kJ/kg$

$c_2$ = specific heat of frozen = $2.5kJ/kg^oC$

$T_1$ = initial temperature of liquid = $2^oC$

$T_2$ = final temperature of liquid = $10^oC$

$T_3$ = initial temperature of frozen = ?

$T_4$ = final temperature of frozen = $2^oC$

Now put all the given value in the above expression, we get:

$6000kJ=[15kg\times 4kJ/kg^oC\times (10-2)^oC]+[15kg\times 275kJ/kg]+[15kg\times 2.5kJ/kg^oC\times (2-T_3)^oC]$

$T_3=-35.2^oC$

Thus, the exit temperature of the product is, $-35.2^oC$