Exam 16: Temperature and Heat

The filament in a light bulb has a diameter of 0.050 mm and an emissivity of 1.0. The temperature of the filament is 3000°C. What should be the length of the filament so it will radiate 60 W of power? The Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴.

A brass rod is 40.1 cm long and an aluminum rod is 79.3 cm long when both rods are at an initial temperature of 0°C. The rods are placed in line with a gap of 0.60 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised until the two rods are barely in contact. The coefficients of linear expansion of brass and aluminum are 2.0 × 10^-5 K^-1 and 2.4 × 10^-5 K-¹, respectively. The temperature at which contact of the rods barely occurs is closest to

When a vapor condenses

The exterior of a supersonic airplane is made of aluminum, which has a coefficient of linear expansion of 24 × 10^-6 K^-1. At 15°C, the plane measures 62.1 m in length. When the plane is in flight, friction with the air increases the temperature of the exterior skin to 200°C. What is the change in the length of the outer skin of the plane?

Two steel spheres are made of the same material and have the same diameter, but one is solid and the other is hollow. If their temperature is increased by the same amount

Betelgeuse is a red supergiant star in the constellation Orion. It radiates heat at the rate of 2.70 × 1030 W and has a surface temperature of 3000 K. Assuming that it is a perfect emitter, what is the radius of Betelgeuse? The Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴.

A 400-g piece of metal at 120.0°C is dropped into a cup containing 450 g of water at 15.0°C. The final temperature of the system is measured to be 40.0°C. What is the specific heat of the metal, assuming no heat is exchanged with the surroundings or the cup? The specific heat of water is 4190 J/(kg∙K).

A certain metal has a coefficient of linear expansion of 2.00 × 10^-5 K^-1. It has been kept in a laboratory oven at 325°C for a long time. It is now removed from the oven and placed in a freezer at -145°C. After it has reached freezer temperature, the percent change in its density during this process is closest to

Suppose that a steel bridge, 1000 m long, was built without any expansion joints and that only one end of the bridge was held fixed. What would the difference in the length of the bridge be between winter and summer, taking a typical winter temperature as 0.00°C, and a typical summer temperature as 40°C? The coefficient of thermal expansion of steel is 10.5 × 10^-6 K^-1.

A cylindrical bar that us well insulated around its sides connects hot and cold reservoirs and conducts heat at a rate of 10.0 J/s under steady state conditions. If all of its linear dimensions (diameter and length) are reduced by half, the rate at which it will now conduct heat between the same reservoirs is closest to

Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10°C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat of water is 4190 J/kg·K. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The specific heat of the alcohol is closest to

If the temperature of an iron sphere is increased

A person pours 330 g of water at 45°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is 900 J/(kg∙K) and that of water is 4190 J/(kg∙K). What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

A 905-g meteor impacts the earth at a speed of 1629 m/s. If all of its energy is entirely converted to heat in the meteor, what will be the resulting temperature rise of the meteor, assuming it does not melt? The specific heat for the meteor material is 472 J/kg∙K, which is about the same as that of iron.

The hole for a bolt in a brass plate has a diameter of 1.200 cm at 20°C. What is the diameter of the hole when the plate is heated to 220°C? The coefficient of linear thermal expansion for brass is 19 × 10^-6/C°. (Express your answer to 4 significant figures.)

A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The room temperature is maintained at -10°C and the outside temperature is 20°C The inside wall is to be covered by a layer of wood in order to reduce the rate of heat loss through the wall BY 90 percent. The thermal conductivities of concrete and wood are 0.80 W/m·K and 0.040 W/m·K, respectively. Under steady state conditions, the thickness of the layer of wood required is closest to

Heat is added to a pure substance in a closed container at a constant rate. The figure shows a graph of the temperature of the substance as a function of time. If Lf = latent heat of fusion and L_v = latent heat of vaporization, what is the value of the ratio L_v / Lf for this substance?

A radiating body originally has a Kelvin temperature T_o, and its surroundings are at 500K (T_o > 500K). If the Kelvin temperature of the radiating body is increased to 3T_o, the net rate at which the body radiates increases by a factor of 333. What was the original temperature T_o?

Some properties of glass are listed here. A glass window pane is 2.7 m high, 2.4 m wide, and 2.0 mm thick. The temperature at the inner surface of the glass is 22°C and at the outer surface 4.0°C. How much heat is lost each hour through the window under steady state conditions?

A machinist needs to remove a tight fitting pin of material A from a hole in a block made of material B. The machinist heats both the pin and the block to the same high temperature and removes the pin easily. What statement relates the coefficient of thermal expansion of material A to that of material B?