The quantity of heat Q that changes the temperature T of a mass m of a substance

Question

The quantity of heat Q that changes the temperature T of a mass m of a substance is given by Q=cmT, where c is the specific heat capacity of the substance. For example, for H2O, c=1cal/gC. 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 0C ice to 0C 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 0C ice water to 0.80 kg of 100C 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 100C boiling water to 0.80 kg of 100C 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 0C ice to 0.80 kg of 100C steam.

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

Explanation / Answer

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 0C ice to 0C 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 0C ice water to 0.80kg of 100C 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 100C boiling water to 0.80kg of 100C 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 0C ice to 0.80kg of 100C steam. To determine this answer, add the last two numbers.

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

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