Question

200-kg cast-iron block at 500 o C is quenched in 400 kg of water at 20 o C. What is the amount of heat into water when the system reaches the thermal equilibrium

Answer 1

The heat gained by water is 41,916 kJ

Step-by-step explanation:

Given;

mass of cast Iron,
`M_c` = 200 kg

mass of water,
`M_w` = 400 kg

initial temperature of the cast iron,
`t_c` = 500 ⁰C

initial temperature of the water,
`t_w` = 20 ⁰C

At thermal equilibrium, the heat lost by the cast iron, is equal to heat gained by the water

`M_cC_p_c(t_c - T_e) = M_wC_p_w(T_e-t_w)\\\\200*460.55(500-T_e) = 400*4200(T_e-20)\\\\92110(500-T_e) = 1680000(T_e-20)\\\\500-T_e = 18.239(T_e - 20)\\\\500-T_e = 18.239T_e - 364.78\\\\T_e + 18.239T_e = 500 + 364.78\\\\19.239T_e = 864.78\\\\T_e = (864.78)/(19.239)\\\\ T_e = 44.95\ ^0C`

The heat gained by water is given by;

Qw = 400 x 4200(44.95 - 20)

Qw = 41916000 J

Qw = 41,916 kJ

Therefore, the heat gained by water is 41,916 kJ