200g of ice is heated from temperature T1= - 20°C to T2= + 110°C. a-Calculate the quantity of heat necessary for this transformation? b-If this heat is provided by the combustion of coal, calculate the mass of coal used?

To solve this problem, we need to consider the different stages of heating: heating the ice to 0°C, melting the ice, heating the water to 100°C, and finally turning the water into steam.

a) Calculate the quantity of heat necessary for this transformation:

1. Heating the ice from -20°C to 0°C: The specific heat capacity of ice is about 2.1 J/g°C. So, the heat (Q1) required can be calculated using the formula Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Q1 = 200g * 2.1 J/g°C * 20°C = 8400 J

2. Melting the ice at 0°C to water at 0°C: The heat of fusion of ice is about 334 J/g. So, the heat (Q2) required to melt the ice can be calculated using the formula Q = mL, where m is the mass and L is the heat of fusion. Q2 = 200g * 334 J/g = 66800 J

3. Heating the water from 0°C to 100°C: The specific heat capacity of water is about 4.18 J/g°C. So, the heat (Q3) required can be calculated using the formula Q = mcΔT. Q3 = 200g * 4.18 J/g°C * 100°C = 83600 J

4. Turning the water into steam at 100°C: The heat of vaporization of water is about 2260 J/g. So, the heat (Q4) required to turn the water into steam can be calculated using the formula Q = mL. Q4 = 200g * 2260 J/g = 452000 J

The total heat required (Q) is the sum of the heats calculated in the four steps: Q = Q1 + Q2 + Q3 + Q4 = 8400 J + 66800 J + 83600 J + 452000 J = 608800 J

b) If this heat is provided by the combustion of coal, calculate the mass of coal used:

The heat of combustion of coal is about 30 MJ/kg, or 30000 J/g. The mass (m) of coal required can be calculated using the formula Q = mc, where Q is the heat required and c is the heat of combustion. m = Q / c = 608800 J / 30000 J/g = 20.29 g

So, about 20.29 g of coal is used.