Question

The quantity of heat Q that changes the temperature ΔT of a mass m of a substance is given by Q=cmΔT, where c is the specific heat capacity of the substance. For example, for H2O, c=1cal/g∘C. And for a change of phase, the quantity of heat Q that changes the phase of a mass m is Q=mL, where L is the heat of fusion or heat of vaporization of the substance. For example, for H2O, the heat of fusion is 80 cal/g (or 80 kcal/kg) and the heat of vaporization is 540 cal/g (or 540 kcal/kg).

A. Use these relationships to determine the number of calories to change 0.80 kg of 0∘C ice to 0∘C ice water.

Express your answer to two significant figures and include the appropriate units.

B. Use these relationships to determine the number of calories to change 0.80 kg of 0∘C ice water to 0.80 kg of 100∘C boiling water.

Express your answer to two significant figures and include the appropriate units.

C. Use these relationships to determine the number of calories to change 0.80 kg of 100∘C boiling water to 0.80 kg of 100∘C steam.

Express your answer to two significant figures and include the appropriate units.

D. Use these relationships to determine the number of calories to change 0.80 kg of 0∘C ice to 0.80 kg of 100∘C steam.

Express your answer to two significant figures and include the appropriate units.

Answer 1

Specific heat 1 cal/(g * ˚C), Heat of fusion 80 cal/g, heat of vaporization = 540 cal/g
Since these numbers are per gram, let’s convert the mass to grams. Mass = 800 grams

a) Use these relationships to determine the number of calories to change 0.80kg of 0∘C ice to 0∘C ice water.

Since the ice is melting, use the following equation.
Q = mass * Hf = 800 * 80 = 64,000 calories

(b) Use these relationships to determine the number of calories to change 0.80kg of 0∘C ice water to 0.80kg of 100∘C boiling water.

In this problem, the ice must melt, And then the temperature of the water must be increased from 0˚ to 100˚. Since we already know the energy that is required to melt the ice, let’s use the following equation to determine the amount of energy that is required to increase its temperature.

Q = mass * Specific heat * ∆T = 800 * 1 * 100 = 80,000 calories
Total = 64,000 + 80,000 = 144,000 calories

(c) Use these relationships to determine the number of calories to change 0.80kg of 100∘C boiling water to 0.80kg of 100∘C steam. Use the following equation.

Q = mass * Hvap = 800 * 540 = 432,000 calories


(d) Use these relationships to determine the number of calories to change 0.80kg of 0∘C ice to 0.80kg of 100∘C steam. To determine this answer, add the last two numbers.

Q = 144,000 + 432,000 = 576,000 calories = 576 Kcal