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In this lesson, we will learn how to relate the mass conversion between liquid and gas states to net heating and the latent heat of vaporization.

Q1:

Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of 500- ∘ C granite must be placed in 4.00 kg of 15.0- ∘ C water to bring its temperature to 100- ∘ C , if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings.

The specific heat capacity of water is 4 1 8 2 / ⋅ J k g C ∘ .

The specific heat capacity of granite is 8 4 0 / ⋅ J k g C ∘ .

The specific latent heat of vaporization of water is 2 2 5 6 kJ/kg.

Q2:

A man consumes 3 0 0 0 kcal of food in one day, converting most of it to thermal energy to maintain body temperature. If he loses half this energy by evaporating water (through breathing and sweating), how many kilograms of water evaporate?

For specific latent heat of vaporization of water, use 2 4 3 0 kJ/kg.

Q3:

A block of ice has a mass of 0.370 kg and is at an initial temperature of − 1 0 . 0 ∘ C . The ice is heated at a rate of 18.0 kW until it reaches a final temperature of 1 6 0 . 0 ∘ C . During the heating to this temperature, the ice undergoes phase changes. In calculating the heating involved in the temperature and phase changes of the ice, use a value of 2 0 9 0 / ⋅ J k g C ∘ for the specific heat capacity of ice, 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water, 1 5 2 0 / ⋅ J k g C ∘ for the specific heat capacity of steam, 333.55 J/g for the specific latent heat of fusion of water, and 2 2 3 0 J/g for the specific latent heat of vaporization of water.

How much heat transfer is required to produce the temperature and phase changes from the initial to the final temperatures and phases?

A stage of the heating of the ice is defined to mean either a time interval in which the ice’s temperature increases while its phase does not change or a time interval in which the ice’s temperature does not change but its phase does change. How long is the third stage?

Q4:

An aluminium pan has a mass of 0.810 kg and is at a temperature of 1 1 2 . 0 ∘ C . A 0.500 kg mass of water with an initial temperature of 2 5 . 0 ∘ C is poured into the pan. If 8.00 g of the water evaporates, determine the equilibrium temperature of the pan and the water, assuming that heat loss by processes other than evaporation is negligible and that the change in mass of water due to evaporation has a negligible effect on the cooling rate of the water. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water, 2 2 3 0 J/g for the specific latent heat of vaporization of water, and 9 0 0 / ⋅ J k g C ∘ for the specific heat capacity of aluminium.

Q5:

A glass cup has a mass of 80.0 g. The cup contains a 275 g mass of coffee that cools from a temperature of 7 0 . 0 ∘ C to 3 5 . 0 ∘ C . Determine how many grams of coffee must evaporate to produce this temperature change, assuming that cooling from all other processes is negligible and that the change in the mass of coffee due to evaporation negligibly affects its cooling rate. Use a value of 2 3 4 0 kJ/kg for the coffee’s heat of vaporization, 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of coffee, and 8 4 0 / ⋅ J k g C ∘ for the specific heat capacity of glass.

Q6:

An aluminum cooking pot with a mass of 2.00 kg contains 1.80 kg of water, to be heated in the cooking pot. The equilibrium temperature of the cooking pot and water is 2 0 . 0 ∘ C before heating begins. The water must be raised to its boiling point and then 0.900 kg of water is boiled away. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water, 2 2 3 0 J/g for the specific latent heat of vaporization of water, and 8 9 7 / ⋅ J k g C ∘ for the specific heat capacity of aluminum. Assume that no heat is lost from the cooking pot during heating.

How much heating is required?

Heat is supplied at a rate of 464 W. How much heating time is required?

Q7:

8.00 g of water vapor condenses on a glass containing both water and 2 . 0 0 × 1 0 2 g of ice. Determine how many grams of the ice will melt as a result. Use a value of 334 kJ/kg for the latent heat of fusion of water and use a value of 2 4 3 0 kJ/kg for the latent heat of vaporization of water.

Q8:

On a certain dry sunny day, a swimming pool’s temperature would rise by if not for evaporation. What fraction of the water must evaporate to carry away precisely enough energy to keep the temperature constant? The specific heat capacity of water is . For specific latent heat of vaporisation of water, use kJ/kg.

Q9:

A storm is modeled as a circle with a radius of 0.850 km that uniformly precipitates 2.5 cm of rain within its circular area. Determine the energy released by condensation occurring in the storm. Use a value of 1 0 0 0 kg/m^{3} for the density of the rainwater and 2 2 3 0 J/g for the rainwater’s heat of vaporization.

Q10:

It is difficult to extinguish a fire on a crude oil tanker, because each litre of crude oil releases J of energy when burned. To illustrate this difficulty, calculate the number of litres of water that must be expended to absorb the energy released by burning 1.00 L of crude oil, if the water’s temperature rises from to , it boils, and the resulting steam’s temperature rises to at constant pressure.

The specific heat capacity of water is .

For specific latent heat of vaporisation of water, use kJ/kg.

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