Problem 28
Suppose you mix 7.00 L of water at \(2.00 \cdot 10^{1}{ }^{\circ} \mathrm{C}\) with \(3.00 \mathrm{~L}\) of water at \(32.0^{\circ} \mathrm{C}\); the water is insulated so that no energy can flow into it or out of it. (You can achieve this, approximately, by mixing the two fluids in a foam cooler of the kind used to keep drinks cool for picnics.) The \(10.0 \mathrm{~L}\) of water will come to some final temperature. What is this final temperature?
Problem 32
A 1.19-kg aluminum pot contains 2.31 L of water. Both pot and water are initially at \(19.7^{\circ} \mathrm{C} .\) How much heat must flow into the pot and the water to bring their temperature up to \(95.0^{\circ} \mathrm{C}\) ? Assume that the effect of water evaporation during the heating process can be neglected and that the temperature remains uniform throughout the pot and the water.
Problem 33
A metal brick found in an excavation was sent to a testing lab for nondestructive identification. The lab weighed the sample brick and found its mass to be \(3.0 \mathrm{~kg} .\) The brick was heated to a temperature of \(3.0 \cdot 10^{2}{ }^{\circ} \mathrm{C}\) and dropped into an insulated copper calorimeter of mass 1.5 kg containing \(2.0 \mathrm{~kg}\) of water at \(2.0 \cdot 10^{1}{ }^{\circ} \mathrm{C} .\) The final temperature at equilibrium was noted to be \(31.7^{\circ} \mathrm{C}\). By calculating the specific heat of the sample from this data, can you identify the brick's material?
Problem 34
A \(2.0 \cdot 10^{2}\) g piece of copper at a temperature of \(450 \mathrm{~K}\) and a \(1.0 \cdot 10^{2} \mathrm{~g}\) piece of aluminum at a temperature of \(2.0 \cdot 10^{2} \mathrm{~K}\) are dropped into an insulated bucket containing \(5.0 \cdot 10^{2} \mathrm{~g}\) of water at \(280 \mathrm{~K}\). What is the equilibrium temperature of the mixture?
Problem 35
When an immersion glass thermometer is used to measure the temperature of a liquid, the temperature reading will be affected by an error due to heat transfer between the liquid and the thermometer. Suppose you want to measure the temperature of \(6.00 \mathrm{~mL}\) of water in a Pyrex glass vial thermally insulated from the environment. The empty vial has a mass of \(5.00 \mathrm{~g}\). The thermometer you use is made of Pyrex glass as well and has a mass of \(15.0 \mathrm{~g}\), of which \(4.00 \mathrm{~g}\) is the mercury inside the thermometer. The thermometer is initially at room temperature \(\left(20.0^{\circ} \mathrm{C}\right) .\) You place the thermometer in the water in the vial and, after a while, you read an equilibrium temperature of \(29.0^{\circ} \mathrm{C} .\) What was the actual temperature of the water in the vial before the temperature was measured? The specific heat capacity of Pyrex glass around room temperature is \(800 . J /(\mathrm{kg} \mathrm{K})\) and that of liquid mercury at room temperature is \(140 . \mathrm{J} /(\mathrm{kg} \mathrm{K})\)
Problem 39
The latent heat of vaporization of liquid nitrogen is about \(200 . \mathrm{kJ} / \mathrm{kg} .\) Suppose you have \(1.00 \mathrm{~kg}\) of liquid nitrogen boiling at \(77.0 \mathrm{~K}\). If you supply heat at a constant rate of \(10.0 \mathrm{~W}\) via an electric heater immersed in the liquid nitrogen, how long will it take to vaporize all of it? What is the time for \(1.00 \mathrm{~kg}\) of liquid helium, whose heat of vaporization is \(20.9 \mathrm{~kJ} / \mathrm{kg}\) ?
Problem 40
Suppose \(0.010 \mathrm{~kg}\) of steam (at \(100.00^{\circ} \mathrm{C}\) ) is added to \(0.10 \mathrm{~kg}\) of water (initially at \(\left.19.0^{\circ} \mathrm{C}\right)\). The water is inside an aluminum cup of mass \(35 \mathrm{~g}\). The cup is inside a perfectly insulated calorimetry container that prevents heat flow with the outside environment. Find the final temperature of the water after equilibrium is reached.
Problem 42
In one of your rigorous workout sessions, you lost \(150 \mathrm{~g}\) of water through evaporation. Assume that the amount of work done by your body was \(1.80 \cdot 10^{5} \mathrm{~J}\) and that the heat required to evaporate the water came from your body. a) Find the loss in internal energy of your body, assuming the latent heat of vaporization is \(2.42 \cdot 10^{6} \mathrm{~J} / \mathrm{kg}\). b) Determine the minimum number of food calories that must be consumed to replace the internal energy lost (1 food calorie \(=4186\) J).
Problem 43
Knife blades are often made of hardened carbon steel. The hardening process is a heat treatment in which the blade is first heated to a temperature of \(1346^{\circ} \mathrm{F}\) and then cooled down rapidly by immersing it in a bath of water. To achieve the desired hardness, after heating to \(1346^{\circ} \mathrm{F}\), a blade needs to be brought to a temperature below \(5.00 \cdot 10^{2}{ }^{\circ} \mathrm{F}\). If the blade has a mass of \(0.500 \mathrm{~kg}\) and the water is in an open copper container of mass \(2.000 \mathrm{~kg}\) and sufficiently large volume, what is the minimum quantity of water that needs to be in the container for this hardening process to be successful? Assume the blade is not in direct mechanical (and thus thermal) contact with the container, and neglect cooling through radiation into the air. Assume no water boils but reaches \(100^{\circ} \mathrm{C} .\) The heat capacity of copper around room temperature is \(c_{\text {copper }}=386 \mathrm{~J} /(\mathrm{kg} \mathrm{K}) .\) Use the data in the table below for the heat capacity of carbon steel
Problem 45
A \(100 .\) mm by \(100 .\) mm by 5.00 mm block of ice at \(0^{\circ} \mathrm{C}\) is placed on its flat face on a 10.0 -mm-thick metal disk that covers a pot of boiling water at normal atmospheric pressure. The time needed for the entire ice block to melt is measured to be \(0.400 \mathrm{~s} .\) The density of ice is \(920 . \mathrm{kg} / \mathrm{m}^{3} .\) Use the data in Table 18.3 to determine the metal the disk is most likely made of
