Question

The formation of condensation on a glass of ice water causes the ice to melt faster than it would otherwise. If 8.00 g of condensation forms on a glass containing both water and 200 g of ice, how many grams of the ice will melt as a result?

Answer 1

Explanation:

It is known that heat (Q) required to change the phase of a given sample of mass m will be as follows.

               $Q_{f} = mL_{f}$    ........ (1)

where,    $L_{f}$ = latent heat of fusion

Similarly,   $Q_{v}$ = mL_{v}[/tex]  ....... (2)

where,     $L_{v}$ = latent heat of vaporization

As it is known that value of latent heat of fusion of water is 334 J/g and latent heat of vaporization of water is 2260 J/g.

Hence, equating both the equations as follows.

          $m_{condensation} \times L_{v}$ = $m_{fusion} \times L_{f}$

          $m_{fusion}$ = $\frac{m_{condensation} \times L_{v}}{L_{f}}$      

                         = $\frac{8 g \times 2260 J/g}{334 J/g}$

                         = 54.13 g

Hence, we can conclude that 54.13 grams of ice will melt.