50 grams of ice cubes at -5oC is added to a 1 litre (1 kg) of water that is initially at 30oC.

a) Use the table of values to find the energy needed to melt the ice:(energy to raise the temperature of the ice to 0oC+ change the state of the ice to water)

b) Hence find the equilibrium temperature of the water and ice mixture

a) To find the energy needed to melt the ice, we have to consider two steps:

Step 1: Raising the temperature of the ice from -5oC to 0oC.

To do this, we need to use the specific heat capacity of ice, which is 2.09 J/g°C. The formula for calculating the energy required to raise the temperature of a substance is:

Energy = mass × specific heat capacity × change in temperature

Given that we have 50 grams of ice and that the change in temperature is 0 - (-5) = 5oC, we can plug these values into the formula:

Energy1 = 50 g × 2.09 J/g°C × 5°C

Step 2: Changing the state of the ice to water.

To change the state of the ice from a solid to a liquid, we need to use the heat of fusion for ice, which is 334 J/g. The formula for calculating the energy needed to change the state of a substance is:

Energy = mass × heat of fusion

Plugging in the values:

Energy2 = 50 g × 334 J/g

To find the total energy needed to melt the ice, we add the two energies:

Total energy = Energy1 + Energy2

b) To find the equilibrium temperature of the water and ice mixture, we need to consider the energy gained by the water and the energy lost by the melting ice.

Let's assume the final temperature is T°C.

The energy gained by the water can be calculated using the formula:

Energy gained by water = mass of water × specific heat capacity of water × (final temperature - initial temperature)

Given that we have 1000 grams (1 kg) of water initially at 30oC, we can plug in the values:

Energy gained by water = 1000 g × 4.18 J/g°C × (T - 30)°C

The energy lost by the melting ice is equal to the total energy needed to melt the ice, which we calculated in part a:

Energy lost by ice = Total energy

To find the equilibrium temperature, we set the energy gained by the water equal to the energy lost by the ice:

Energy gained by water = Energy lost by ice

1000 g × 4.18 J/g°C × (T - 30)°C = Total energy

Now we can solve this equation for T to find the equilibrium temperature of the water and ice mixture.