Answer:
T = 30.42°C
Explanation:
According to the conservation of energy principle:
[tex]Energy\ Given\ by\ Resistor = Heat\ Gain\ by\ Copper + Heat\ Gain\ by\ Water\\E = m_{c}C_{c}(T_{2c} - T_{1c}) + m_{w}C_{w}(T_{2w} - T_{1w})[/tex]
E = 120 KJ
mc = mass of copper = 13 kg
Cc = specific heat capacity of copper = 0.385 KJ/kg.°C
T2c = T2w = Final Equilibrium Temperature = T = ?
T1c = Initial Temperature of Copper = 27°C
T1w = Initial Temperature of Water = 50°C
mw = mass of water = 4 kg
Cw = specific heat capacity of water = 4.2 KJ/kg.°C
Therefore,
[tex]120\ KJ = (13\ kg)(0.385\ KJ/kg^oC)(T-27^oC) + (4\ kg)(4.2\ KJ/kg^oC)(T-50^oC)\\120\ KJ - 135.135\ KJ - 840\ KJ = (- 5.005T - 16.8 T)\ KJ/^oC\\T = \frac{-855.135\ KJ}{-28.105\ KJ/^oC}\\[/tex]
T = 30.42°C
