14.3 Phase Change and Latent Heat

Why does snow remain on mountain slopes even when daytime temperatures are higher than the freezing temperature?

How much heat transfer (in kilocalories) is required to thaw a 0.450-kg package of frozen vegetables originally at $0º \text{C}$ if their heat of fusion is the same as that of water?

(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 $\text{30} . 0º \text{C}$ 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 $1 \text{watt}\textrm{ }=\textrm{ }\text{1}\textrm{ } \text{joule}/\text{second} \left(\text{1}\textrm{ }\text{W}\textrm{ }=\textrm{ }\text{1}\textrm{ }\text{J}/\text{s}\right)$?

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 $\text{1}\textrm{ }\text{watt}\textrm{ }=\textrm{ }\text{1}\textrm{ }\text{joule}/\text{second} \left(\text{1}\textrm{ }\text{W}\textrm{ }=\textrm{ }\text{1}\textrm{ }\text{J}/\text{s}\right)$?

(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 $\text{130}º \text{C}$, 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.

How many grams of coffee must evaporate from 350 g of coffee in a 100-g glass cup to cool the coffee from $\text{95} . 0º \text{C}$ to $\text{45} . 0º \text{C}$? 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.)

(a) It is difficult to extinguish a fire on a crude oil tanker, because each liter of crude oil releases $2 . \text{80} \times \text{10}^{7} \text{J}$ 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 $\text{20} . 0º \text{C}$ to $\text{100}º \text{C}$, it boils, and the resulting steam is raised to $\text{300}º \text{C}$. (b) Discuss…

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 $3 .\text{35}\textrm{ }\text{kJ}/\text{kg} ⋅º \text{C}$, and assume that no phase change occurs.

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

Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of $\text{500}º \text{C}$ rock must be placed in 4.00 kg of $\text{15} . 0º \text{C}$ water to bring its temperature to $\text{100}º \text{C}$, 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.

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 $\text{808} \textrm{ }\text{kg}/\text{m}^{3}$.

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