Ch 19: Work, Heat, and the First Law of Thermodynamics
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Problem 19
A 65 cm^3 block of iron is removed from an 800°C furnace and immediately dropped into 200 mL of 20°C water. What fraction of the water boils away?Problem 19
The ends of a 20-cm-long, 2.0-cm-diameter rod are maintained at 0°C and 100°C by immersion in an ice-water bath and boiling water. Heat is conducted through the rod at 4.5×10^4 J per hour. Of what material is the rod made?Problem 19
You are boiling pasta and absentmindedly grab a copper stirring spoon rather than your wooden spoon. The copper spoon has a 20 mm ×1.5 mm rectangular cross section, and the distance from the boiling water to your 35°C hand is 18 cm. How long does it take the spoon to transfer 25 J of energy to your hand?
Problem 19
30 g of copper pellets are removed from a 300°C oven and immediately dropped into 100 mL of water at 20°C in an insulated cup. What will the new water temperature be?Problem 19
512 g of an unknown metal at a temperature of 15°C is dropped into a 100 g aluminum container holding 325 g of water at 98°C. A short time later, the container of water and metal stabilizes at a new temperature of 78°C. Identify the metal.Problem 19
The beaker in FIGURE P19.45, with a thin metal bottom, is filled with 20 g of water at 20°C. It is brought into good thermal contact with a 4000 cm^3 container holding 0.40 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings. What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome.Problem 19
A typical nuclear reactor generates 1000 MW (1000 MJ/s) of electric energy. In doing so, it produces 2000 MW of 'waste heat' that must be removed from the reactor to keep it from melting down. Many reactors are sited next to large bodies of water so that they can use the water for cooling. Consider a reactor where the intake water is at 18°C. State regulations limit the temperature of the output water to 30°C so as not to harm aquatic organisms. How many liters of cooling water have to be pumped through the reactor each minute?Problem 19
Liquid helium, with a boiling point of 4.2 K, is used in ultralow-temperature experiments and also for cooling the superconducting magnets used in MRI imaging in medicine. Storing liquid helium so far below room temperature is a challenge because even a small 'heat leak' will boil the helium away. A standard helium dewar, shown in FIGURE P19.67, has an inner stainless-steel cylinder filled with liquid helium surrounded by an outer cylindrical shell filled with liquid nitrogen at –196°C. The space between is a vacuum. The small structural supports have very low thermal conductivity, so you can assume that radiation is the only heat transfer between the helium and its surroundings. Suppose the helium cylinder is 16 cm in diameter and 30 cm tall and that all walls have an emissivity of 0.25. The density of liquid helium is 125 kg/m^3 and its heat of vaporization is 2.1×10^4 J/kg. a. What is the mass of helium in the filled cylinder?Problem 19
Most stars are main-sequence stars, a group of stars for which size, mass, surface temperature, and radiated power are closely related. The sun, for instance, is a yellow main-sequence star with a surface temperature of 5800 K. For a main-sequence star whose mass M is more than twice that of the sun, the total radiated power, relative to the sun, is approximately P/Pₛᵤₙ=1.5(M/Mₛᵤₙ)^3.5 . The star Regulus A is a bluish main-sequence star with mass 3.8Mₛᵤₙ and radius 3.1Rₛᵤₙ. What is the surface temperature of Regulus A?Problem 19
A 750 g aluminum pan is removed from the stove and plunged into a sink filled with 10.0 L of water at 20.0°C . The water temperature quickly rises to 24.0°C. What was the initial temperature of the pan in °C and in °F?Problem 19
10 g of aluminum at 200°C and 20 g of copper are dropped into 50 cm^3 of ethyl alcohol at 15°C. The temperature quickly comes to 25°C . What was the initial temperature of the copper?Problem 19
A lava flow is threatening to engulf a small town. A 400-m-wide, 35-cm-thick tongue of 1200°C lava is advancing at the rate of 1.0 m per minute. The mayor devises a plan to stop the lava in its tracks by flying in large quantities of 20°C water and dousing it. The lava has density 2500 kg/m^3, specific heat 1100 J/kg K, melting temperature 800°C, and heat of fusion 4.0×10^5 J/kg. How many liters of water per minute, at a minimum, will be needed to save the town?Problem 19
10 g of steam at the boiling point are combined with 50 g of ice at the freezing point. What is the final temperature of the system?Problem 19
0.25 mol of a gas are compressed at a constant pressure of 250 kPa from 6000 cm^3 to 2000 cm^3, then expanded at a constant temperature back to 6000 cm^3. What is the net work done on the gas?Problem 19
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. a. What are the gas volume and temperature after the expansion?Problem 19
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. b. How much heat energy is transferred to the gas to cause this expansion?Problem 19
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. c. What is the gas pressure after the decrease?Problem 19
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. d. What amount of heat energy is transferred from the gas as its pressure decreases?Problem 19
500 J of heat energy are transferred to a gas during a process in which the gas expands at constant pressure from 400 cm^3 to 800 cm^3 . The gas's thermal energy increases by 300 J during this process. What is the gas pressure?Problem 19
FIGURE CP19.80 shows a thermodynamic process followed by 0.015 mol of hydrogen. How much heat energy is transferred to the gas?Problem 19
An ideal-gas process is described by p=cV^ /2, where c is a constant. a.Find an expression for the work done on the gas in this process as the volume changes from V₁ to V₂.Problem 19
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (a) the final temperature,Problem 19
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (b) the work done on the gas, andProblem 19
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (c) the heat energy transferred to the gas?Problem 19
An ideal-gas process is described by p=cV^ /2, where c is a constant. b. 0.033 mol of gas at an initial temperature of 150°C is compressed, using this process, from 300 cm^3 to 200 cm^3. How much work is done on the gas?Problem 19
80 J of work are done on the gas in the process shown in FIGURE EX19.3. What is V₁ in cm^3?Problem 19
A gas cylinder holds 0.10 mol of O₂ at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the pressure is halved. What are the final (b) temperature?Problem 19
The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. a. What is the specific heat ratio γ?Problem 19
A gas cylinder holds 0.10 mol of O₂ at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the volume is doubled. What are the final (a) pressure andProblem 19
0.10 mol of nitrogen gas follow the two processes shown in FIGURE P19.58. How much heat is required for each?
