Question

A workman needs to know the temperature inside the oven. He removes 2.0-lb. iron bar from the oven and places in a 1-lb aluminum container partially filled with 2.0 lb. of water. If the temperature of the water rises from 70 to 120^oF, what was the oven temperature?

Answer 1

Given

Specific heat of iron: 0.11 Btu/(lb·°F)

Specific heat of aluminum: 0.258 Btu/(lb·°F)

Solution

Heat from iron as it cools:

$$Q_1=c_im_i(t-t_i).$$

Heat to the container and water as they heat up:

$$Q_2=c_wm_w(t-t_w)+c_am_a(t-t_w).$$

The heat flows result in 0:

$$Q_1+Q_2=0,\\ c_im_i(t-t_i)+c_wm_w(t-t_w)+c_am_a(t-t_w)=0,\\\space\\ t_i=\frac{(t-t_w)(c_wm_w+c_am_a)+c_im_it}{c_im_i}=633°\text{F}.$$