Question

A black smith drop 2kg of iron rod at temperature of 260°c into water raising the temperature 60°c if the heat capacity of the rod is 4.2 the specific heat capacity of 4200.find the mass of the water

Answer 1

Water will heated, while the iron rod will cooled. We can write the heat balance equation (we don't know the initial temperature of the water, so let's assume $t_w=30^{\circ}C$):

$$m_wc_w(T_m-t_w)=m_ic_i(t_i-T_m),$$ $$m_w=\dfrac{m_ic_i(t_i-T_m)}{c_w(T_m-t_w)},$$ m_w=\dfrac{2\ kg\cdot460\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot(260^{\circ}C-60^{\circ}C)}{4200\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot(60^{\circ}C-30^{\circ}C)}=1.46\ kg.