Review. A 670-kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is –15.0°C and it moves at 14.0 km/s relative to the planet. As it crashes into the Earth, assume the internal energy transformed from the mechanical energy of the meteoroid-Earth system is shared equally between the meteoroid and the Earth and all the material of the meteoroid rises momentarily to the same final temperature. Find this temperature. Assume the specific heat of liquid and of gaseous aluminum is 1 170 J/kg · °C.
The value of the final temperature.
Answer to Problem 20.73AP
The value of the final temperature is
Explanation of Solution
Given info: The mass of the meteorite is
Write the expression for the gravitational potential enegy.
Here,
Write the expression for the kinetic enegy.
Here,
Write the expression for the loss of mechanical energy of the meteorite.
Substitute
Substitute
Thus, the loss of mechanical energy is
The value of the internal energy is half of the loss of mechanical energy.
Write the expression for the internal energy.
Substitute
Thus, the internal energy is
Write the expression for the energy required to increase the temperature.
Here,
Write the expression for the rate of energy required during a phase change.
Here,
For the energy required to raise the temperature to a melting point.
Substitute
Thus, the energy required to raise the temperature to a melting point is
For the energy required to melt the meteorite.
Substitute
Thus, the energy required to melt the meteorite is
For the energy required to raise the temperature to a boiling point.
Substitute
Thus, the energy required to raise the temperature to a boiling point is
For the energy required to boil the meteorite.
Substitute
Thus, the energy required to boil the meteorite is
Write the expression for the internal energy change for the meteorite.
Substitute
Conclusion:
Therefore, the value of the final temperature is
Want to see more full solutions like this?
Chapter 20 Solutions
Physics for Scientists and Engineers
- If a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) None of those statements is true.arrow_forwardA 100-kg steel support rod in a building has a length of 2.0 m at a temperature of 20°C. The rod supports a hanging load of 6 000 kg. Find (a) the work done on the rod as the temperature increases to 40°C, (b) the energy Q added to the rod (assume the specific heat of steel is the same as that for iron), and (c) the change in internal energy of the rod.arrow_forwardCompressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is 6.3 x 105 m³, 5 and the pressure of the air in it is 7.4 × 106 Pa. Assume that air is a diatomic ideal gas whose internal energy U is given by U = nRT. If one home uses 30.0 kWh of energy per day, how many homes could this internal energy serve for one day?arrow_forward
- A weightlifter drinks a protein shake that contains 2.00 × 10² Calories. She then performs multiple repetitions on the bench press and does 2.75 x 105 J of work. After her workout, her net change in internal energy is +1.50 × 105 J. During her workout, she loses heat to the environment, which results in the vaporization of perspiration from the surface of her skin. What mass of water did she lose due to perspiration? Assume the latent heat of vaporization of the perspiration is 2.42 x 106 J/kg. Number Unitsarrow_forwardA 25 g ball is released from rest 80 m above the surface of Earth. During the fall the total internal energy of the ball and air increases by 15 J. What is the velocity of the ball in m/s just before it hits the surface? (Assume that the air resistance force is constant during the movement and g-10 m/s) Option1 Option2 Option3 Option4 Option5 20 30 36 40 44arrow_forwardA room has a pine ceiling [ k = 0.12 W/(m•C°) ] that measures 3.0 m 4.0 m 2.0 cm. On a cold day, the temperature inside the room is 20°C, and the temperature in the attic above is 8°C. If 6.0 cm of glass wool insulation [ k = 0.042 W/(m•C°) ] were put in above the ceiling, how much energy would be saved in one hour? Please use gresa methodarrow_forward
- A steel block of mass m is given a push so that it initially slides along a horizontal, steel track of mass M with speed v_0. The block and the track have the same specific heat c. After the initial push, the only forces acting on the block are its weight, a normal force from the track, and friction with the track (coefficient of kinetic friction μ_k). The block travels some distance before coming to rest. Both the block and the track are initially at a temperature T_0 and both end up at a temperature T_1 after the block has come to rest. You may assume that no heat leaves the block + track system and the the only source of heat to increase the temperatures is mechanical energy dissipated by friction. Which of the following changes to the given values would lead to the biggest increase in T_1, assuming all other parameters are left unchanged? (You may ignore any effects of thermal expansion.) a. increase v_0 by 20% b. increase μ_k by 50% c. increase both m and M by 15% d. increase…arrow_forwardA solar collector is placed in direct sunlight where it absorbs energy at the rate of 840 J/s for each square meter of its surface. The emissivity of the solar collector is e = 0.66. What equilibrium temperature does the collector reach? Assume that the only energy loss is due to the emission of radiation.arrow_forwardImagine a physics lecture hall with 83 students who are settling in for a 1-hour lecture. At the start of the lecture, the temperature of the air in the room is a comfortable 70oF (21.1°C). Unfortunately, the room’s air conditioner breaks right as the lecture begins. Each student has an average power output of about 60.0 W at room temperature. Imagine the energy released by each student goes into heating just the air in the room, which has a volume of 9.50 × 102 m3 and a density of 1.20 kg/m3. Assume the volume of the air remains constant and the specific heat capacity of the air is 718 J/(kg · °C). Calculate the room’s temperature at the end of the lecture in oF (the answer may sound high (!), but in reality, a significant portion of the heat produced would be absorbed by the walls, ceiling, floors, chairs, desks, and so on, which we are neglecting).arrow_forward
- A solar hot-water-heating system consists of a hot-water tank and a solar panel. The tank is well insulated and has a time constant of 60 hr. The solar panel generates 2200 Btu/hr during the day, and the tank has a heat capacity of 3°F per thousand Btu. If the water in the tank is initially 105°F and the room temperature outside the tank is 81°F, what will be the temperature in the tank after 10 hr of sunlight? What is U(t), the rate of temperature change due to the solar heating panel? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. U(t)= °F/hr OB. U(t) is unknown. xample Get more help Clear all Check answerarrow_forwardA 1.0 x 102-kg steel support rod in a building has a length of 2.0 m at a temperature of 20.0°C. The rod supports a hanging load of 6.0 x 103 kg. Find (a) the work done on the rod as the temperature increases to 40.0°C, (b) the energy Q added to the rod (assume the specific heat of steel is the same as that for iron), and (c) the change in internal energy of the rod.arrow_forwardIn an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 12.4 oC. The temperature at the inside surface of the wall is 18.4 oC. The wall is 0.13 m thick and has an area of 8.4 m2. Assume that one kilowatt hour of electrical energy costs $0.10. How many hours are required for one dollar's worth of energy to be conducted through the wall?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning