# 14.3 Phase change and latent heat  (Page 6/9)

 Page 6 / 9

A bag containing $0º\text{C}$ ice is much more effective in absorbing energy than one containing the same amount of $0º\text{C}$ water.

1. How much heat transfer is necessary to raise the temperature of 0.800 kg of water from $0º\text{C}$ to $\text{30}\text{.}0º\text{C?}$
2. How much heat transfer is required to first melt 0.800 kg of $0º\text{C}$ ice and then raise its temperature?
3. Explain how your answer supports the contention that the ice is more effective.

(a) How much heat transfer is required to raise the temperature of a 0.750-kg aluminum pot containing 2.50 kg of water from $\text{30}\text{.}0º\text{C}$ to the boiling point and then boil away 0.750 kg of water? (b) How long does this take if the rate of heat transfer is 500 W ?

(a) 591 kcal

(b) $4\text{.}\text{94}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{s}$

The formation of condensation on a glass of ice water causes the ice to melt faster than it would otherwise. If 8.00 g of condensation forms on a glass containing both water and 200 g of ice, how many grams of the ice will melt as a result? Assume no other heat transfer occurs.

On a trip, you notice that a 3.50-kg bag of ice lasts an average of one day in your cooler. What is the average power in watts entering the ice if it starts at $0º\text{C}$ and completely melts to $0º\text{C}$ water in exactly one day ?

13.5 W

On a certain dry sunny day, a swimming pool’s temperature would rise by $1\text{.}\text{50º}\text{C}$ if not for evaporation. What fraction of the water must evaporate to carry away precisely enough energy to keep the temperature constant?

(a) How much heat transfer is necessary to raise the temperature of a 0.200-kg piece of ice from $-\text{20.}0º\text{C}$ to $\text{130º}\text{C}$ , including the energy needed for phase changes?
(b) How much time is required for each stage, assuming a constant 20.0 kJ/s rate of heat transfer?
(c) Make a graph of temperature versus time for this process.

(a) 148 kcal

(b) 0.418 s, 3.34 s, 4.19 s, 22.6 s, 0.456 s

In 1986, a gargantuan iceberg broke away from the Ross Ice Shelf in Antarctica. It was approximately a rectangle 160 km long, 40.0 km wide, and 250 m thick.

(a) What is the mass of this iceberg, given that the density of ice is ?

(b) How much heat transfer (in joules) is needed to melt it?

(c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of , 12.00 h per day?

How many grams of coffee must evaporate from 350 g of coffee in a 100-g glass cup to cool the coffee from $\text{95}\text{.}0º\text{C}$ to $\text{45}\text{.}0º\text{C}$ ? You may assume the coffee has the same thermal properties as water and that the average heat of vaporization is 2340 kJ/kg (560 cal/g). (You may neglect the change in mass of the coffee as it cools, which will give you an answer that is slightly larger than correct.)

33.0 g

(a) It is difficult to extinguish a fire on a crude oil tanker, because each liter of crude oil releases $2\text{.}\text{80}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{J}$ of energy when burned. To illustrate this difficulty, calculate the number of liters of water that must be expended to absorb the energy released by burning 1.00 L of crude oil, if the water has its temperature raised from $\text{20}\text{.}0º\text{C}$ to $\text{100º}\text{C}$ , it boils, and the resulting steam is raised to $\text{300º}\text{C}$ . (b) Discuss additional complications caused by the fact that crude oil has a smaller density than water.

(a) 9.67 L

(b) Crude oil is less dense than water, so it floats on top of the water, thereby exposing it to the oxygen in the air, which it uses to burn. Also, if the water is under the oil, it is less efficient in absorbing the heat generated by the oil.

The energy released from condensation in thunderstorms can be very large. Calculate the energy released into the atmosphere for a small storm of radius 1 km, assuming that 1.0 cm of rain is precipitated uniformly over this area.

To help prevent frost damage, 4.00 kg of $0º\text{C}$ water is sprayed onto a fruit tree.

(a) How much heat transfer occurs as the water freezes?

(b) How much would the temperature of the 200-kg tree decrease if this amount of heat transferred from the tree? Take the specific heat to be , and assume that no phase change occurs.

a) 319 kcal

b) $2\text{.}\text{00º}\text{C}$

A 0.250-kg aluminum bowl holding 0.800 kg of soup at $\text{25}\text{.}0º\text{C}$ is placed in a freezer. What is the final temperature if 377 kJ of energy is transferred from the bowl and soup, assuming the soup’s thermal properties are the same as that of water? Explicitly show how you follow the steps in Problem-Solving Strategies for the Effects of Heat Transfer .

A 0.0500-kg ice cube at $-\text{30}\text{.}0º\text{C}$ is placed in 0.400 kg of $\text{35}\text{.}0º\text{C}$ water in a very well-insulated container. What is the final temperature?

$\text{20.6º}\text{C}$

If you pour 0.0100 kg of $\text{20}\text{.}0º\text{C}$ water onto a 1.20-kg block of ice (which is initially at $-\text{15}\text{.}0º\text{C}$ ), what is the final temperature? You may assume that the water cools so rapidly that effects of the surroundings are negligible.

Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of $\text{500º}\text{C}$ rock must be placed in 4.00 kg of $\text{15}\text{.}0º\text{C}$ water to bring its temperature to $\text{100º}\text{C}$ , if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings and take the average specific heat of the rocks to be that of granite.

4.38 kg

What would be the final temperature of the pan and water in Calculating the Final Temperature When Heat Is Transferred Between Two Bodies: Pouring Cold Water in a Hot Pan if 0.260 kg of water was placed in the pan and 0.0100 kg of the water evaporated immediately, leaving the remainder to come to a common temperature with the pan?

In some countries, liquid nitrogen is used on dairy trucks instead of mechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid nitrogen, which has a density of .

(a) Calculate the heat transfer necessary to evaporate this amount of liquid nitrogen and raise its temperature to $3\text{.}\text{00º}\text{C}$ . (Use ${c}_{p}$ and assume it is constant over the temperature range.) This value is the amount of cooling the liquid nitrogen supplies.

(b) What is this heat transfer rate in kilowatt-hours?

(c) Compare the amount of cooling obtained from melting an identical mass of $0º\text{C}$ ice with that from evaporating the liquid nitrogen.

(a) $1\text{.}\text{57}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{kcal}$

(b) $\text{18}\text{.3 kW}\cdot \text{h}$

(c) $1\text{.}\text{29}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{kcal}$

Some gun fanciers make their own bullets, which involves melting and casting the lead slugs. How much heat transfer is needed to raise the temperature and melt 0.500 kg of lead, starting from $\text{25}\text{.}0º\text{C}$ ?

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