1.5 Phase changes  (Page 9/20)

(a) How much heat transfer is necessary to raise the temperature of a 0.200-kg piece of ice from $\mathrm{-20.0}\text{°}\text{C}$ to $130.0\text{°}\text{C}$ , 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.

In 1986, an enormous iceberg broke away from the Ross Ice Shelf in Antarctica. It was an approximately rectangular prism 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 $917{\text{kg/m}}^3$ ? (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 $100{\text{W/m}}^2$ , 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 and the cup from $95.0\text{°}\text{C}$ to $45.0\text{°}\text{C}$ ? Assume the coffee has the same thermal properties as water and that the average heat of vaporization is 2340 kJ/kg (560 kcal/g). Neglect heat losses through processes other than evaporation, as well as the change in mass of the coffee as it cools. Do the latter two assumptions cause your answer to be higher or lower than the true answer?

(a) It is difficult to extinguish a fire on a crude oil tanker, because each liter of crude oil releases $2.80\times {10}^7\text{J}$ 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’s temperature rises from $20.0\text{°}\text{C}$ to $100\text{°}\text{C}$ , it boils, and the resulting steam’s temperature rises to $300\text{°}\text{C}$ at constant pressure. (b) Discuss additional complications caused by the fact that crude oil is less dense than water.

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 water at $0\text{°}\text{C}$ 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 $3.35\text{kJ/kg}·\text{°}\text{C}$ , and assume that no phase change occurs in the tree.

A 0.250-kg aluminum bowl holding $0.800\text{kg}$ of soup at $25.0\text{°}\text{C}$ is placed in a freezer. What is the final temperature if 388 kJ of energy is transferred from the bowl and soup, assuming the soup’s thermal properties are the same as that of water?

A 0.0500-kg ice cube at $\mathrm{-30.0}\text{°}\text{C}$ is placed in 0.400 kg of $35.0\text{-}\text{°}\text{C}$ water in a very well-insulated container. What is the final temperature?

If you pour 0.0100 kg of $20.0\text{°}\text{C}$ water onto a 1.20-kg block of ice (which is initially at $\mathrm{-15.0}\text{°}\text{C}$ ), 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 $500\text{-}\text{°}\text{C}$ granite must be placed in 4.00 kg of $15.0\text{-}\text{°}\text{C}$ water to bring its temperature to $100\text{°}\text{C}$ , if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings.

What would the final temperature of the pan and water be in [link] if 0.260 kg of water were 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?