How much energy is needed to melt a 50kg snowman at -2 degrees Celsius?

[Simple_Simon]

I have a simple physics problem I'm not sure how to solve.

A child builds a big snowman which contains 50kg of snow. How much energy would it take to melt it from an initial temperature of -2 degrees Celsius?

 

[Doc Al]

A child builds a big snowman which contains 50kg of snow. How much energy would it take to melt it from an initial temperature of -2 degrees Celsius?

Solve it in two steps. First find the heat needed to raise the temperature of the ice from -2 to 0 degrees C:
Q_1 = mc_{ice}\Delta t (c_{ice} is the specific heat of ice/snow)
Then find the heat needed to melt the ice:
Q_2 = mL_{water} (L_{water} is the latent heat of fusion for water-ice)

 

[M98Ranger]

To solve this problem, we need to use the specific heat capacity of water and the heat of fusion for water, as well as the formula for calculating energy.

First, let's convert the initial temperature from Celsius to Kelvin by adding 273.15 to -2, giving us 271.15K.

Next, we need to determine the amount of energy needed to raise the temperature of the snowman from -2 degrees Celsius (271.15K) to its melting point of 0 degrees Celsius (273.15K). This can be calculated using the specific heat capacity of water, which is 4.186 joules/gram*Kelvin.

So, the energy needed to raise the temperature of 50kg of snow by 2 degrees Celsius would be:
(50kg)(4.186 joules/gram*Kelvin)(2K) = 418.6 kilojoules.

Next, we need to determine the amount of energy needed to melt the snowman. The heat of fusion for water is 334 kilojoules/kg. Therefore, the energy needed to melt 50kg of snow would be:
(50kg)(334 kilojoules/kg) = 16,700 kilojoules.

Finally, to find the total energy needed to melt the snowman, we add the two values we calculated:
418.6 kilojoules + 16,700 kilojoules = 17,118.6 kilojoules.

So, it would take approximately 17,118.6 kilojoules of energy to melt a snowman made of 50kg of snow starting at -2 degrees Celsius.