Answer to Question #120009 in Physics for Susan Williams

Question

A copper calorimeter of mass 60 g contains 35 g of water and 5 g of ice at 00C. What mass of steam 1000C passed into the calorimeter will raise the temperature to 30oC. (Specific latent heats of ice = 320 J/g, of steam = 2200 J/g; Specific heat capacity of copper = 0.4 J/gK).

Answer 1

The system receives heat from the steam. The ice melts and heats up, the water and calorimeter heat up from 0 to 30°C. Meanwhile the steam cools, condenses, and turns into water:

$$m_s\lambda _s=m_wc_w\Delta t+m_ic_i\Delta t+m_cc_c\Delta t+m_iL_i,\\ m_s=\frac{\Delta t(m_wc_w+m_ic_i+m_cc_c)+m_iL_i}{\lambda_s}=\\\space\\ =\frac{(35-0)(35\cdot4.2+5\cdot2.1+60\cdot0.4)+5\cdot320}{2200}=3.2\text{ g}.$$