A. How many calories are needed to raise the temperature of 1 gram of water by 1 °C?

B. How many calories are needed to melt 1 gram of ice at 0 °C?

C. How many calories are needed to vaporize 1 gram of boiling water at 100 °C?

A) 1 cal

B) 80 cal

C) 540 cal

Explanation:

A)

The amount of heat energy needed to raise the temperature of a certain mass of a substance is given by

where

m is the mass of the substance

C is the specific heat capacity

is the change in temperature

In this problem:

m = 1 g is the mass of water

is  the specific heat capacity of water

is the change in temperature

So, the heat needed is

B)

For a solid substance at its melting point, the amount of heat needed to melt completely the substance is given by

where

m is the mass of the substance

is the specific latent heat of fusion of the substance

In this problem:

- The ice is already at melting point, 0 °C

- Mass of the ice:

- Specific latent heat of fusion of ice:

So, the heat needed is

C)

For a liquid substance at its boiling point, the amount of heat needed to boil completely the substance is given by

where

m is the mass of the substance

is the specific latent heat of vaporization of the substance

In this problem:

- The water is already at boiling point, 100 °C

- Mass of the water:

- Specific latent heat of vaporization of water:

So, the heat needed is