Answer to Question #107367 in Molecular Physics | Thermodynamics for Nyx

Question

A jar of tea is placed in sunlight until it
reaches an equilibrium temperature of 33.4◦C .
In an attempt to cool the liquid, which has a
mass of 184 g , 103 g of ice at 0.0◦C is added.
At the time at which the temperature of the
tea is 32.6◦C , find the mass of the remaining ice in the jar. The specific heat of water
is 4186 J/kg ·◦ C . Assume the specific heat
capacity of the tea to be that of pure liquid
water.
Answer in units of g.

Answer 1

The heat balance equation says

$c_wm_w(t_i-t_f)=\lambda_{ice}\Delta m_{ice}.$

Hence

$\Delta m_{ice}=\frac{c_wm_w(t_i-t_f)}{\lambda_{ice}}\\ =\frac{4.186\times 184\times(33.4-32.6)}{334}=1.84\:\rm g.$

The mass of the remaining ice in the jar

$m=103-1.84=101\:\rm g.$