Question

Suppose you take a 50gram ice cube from the freezer at an initial temperature of -20°C. How much energy would it take to completely vaporize the ice cube? (Hint: think of this process as four separate steps and calculate the energy needed for each one.)

Answer 1

Answer:

The amount of energy required is $152.68\times 10^{3}Joules$

Explanation:

The energy required to convert the ice to steam is the sum of:

1) Energy required to raise the temperature of the ice from -20 to 0 degree Celsius.

2) Latent heat required to convert the ice into water.

3) Energy required to raise the temperature of water from 0 degrees to 100 degrees

4) Latent heat required to convert the water at 100 degrees to steam.

The amount of energy required in each process is as under

1) $Q_1=mass\times S.heat_{ice}\times \Delta T\\\\Q_1=50\times 2.05\times 20=2050Joules$

where

$'S.heat_{ice}$' is specific heat of ice =$2.05J/^{o}C\cdot gm$

2) Amount of heat required in phase 2 equals

$Q_2=L.heat\times mass\\\\\therefore Q_{2}=334\times 50=16700Joules$

3) The amount of heat required to raise the temperature of water from 0 to 100 degrees centigrade equals

$Q_3=mass\times S.heat\times \Delta T\\\\Q_1=50\times 4.186\times 100=20930Joules$

where

$'S.heat_{water}$' is specific heat of water=$4.186J/^{o}C\cdot gm$

4) Amount of heat required in phase 4 equals

$Q_4=L.heat\times mass\\\\\therefore Q_{4}=2260\times 50=113000Joules$Thus the total heat required equals $Q=Q_{1}+Q_{2}+Q_{3}+Q_{4}\\\\Q=152.68\times 10^{3}Joules$