Exam 12: Thermal Properties of Matter

A solid cylindrical bar conducts heat at a rate of 25 W from a hot to a cold reservoir under steady state conditions. If both the length and the diameter of this bar are doubled, the rate at which it will conduct heat between these reservoirs will be

The radius of a star is 6.95 × 10⁸ m, and its rate of radiation has been measured to be 5.32 × 10²⁶ W. Assuming that it is a perfect emitter, what is the temperature of the surface of this star? (σ = 5.67 × 10^-8 W/m² ∙ K⁴)

A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper, with the aluminum and the copper in thermal contact. The specific heat capacity of aluminum is more than double that of copper. Which object experiences the greater magnitude gain or loss of heat during the time the system takes to reach thermal equilibrium?

The thermal conductivity of a certain concrete is 0.80 W/m . K and the thermal conductivity of a certain wood is 0.10 W/m ∙ K. How thick would a solid concrete wall have to be in order to have the same rate of heat flow through it as an 8.0-cm thick wall made of solid wood? Both walls have the same surface area and the same temperature difference across their faces.

What is the average translational kinetic energy of an ideal gas at $819 \mathrm {~K} \text { ? }$ The Boltzmann constant is 1.38 × 10^-23 J/K.

An 920-g piece of iron at 100°C is dropped into a calorimeter of negligible heat capacity containing 50 g of ice at 0°C and 92 g of water, also at 0°C. What is the final temperature of the system? The specific heat of iron is 448 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the latent heat of fusion of water is 33.5 × 10⁴ J/kg.

The water flowing over Niagara Falls drops a distance of 50 m. If all the gravitational potential energy is converted to thermal energy, by what temperature does the water rise? The specific heat of water is 4186 J/kg ∙ K.

How many grams of ice at -17°C must be added to 741 grams of water that is initially at a temperature of $70 ^ { \circ } \mathrm { C }$ to produce water at a final temperature of $12 ^ { \circ } \mathrm { C } \text { ? }$ Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is 4190 J/kg ∙ C° and of ice is 2000 J/kg ∙ C°. For water the normal melting point is 0°C and the heat of fusion is 334 × 10³ J/kg. The normal boiling point is 100°C and the heat of vaporization is 2.256 × 10⁶ J/kg.

The process shown on the pV diagram in the figure is

The figure shows a pV diagram for 0.98 mol of ideal gas that undergoes the process 1 → 2. The gas then undergoes an isochoric heating from point 2 until the pressure is restored to the value it had at point 1. What is the final temperature of the gas? (R = 8.31 J/mol ∙ K).

Solar houses use a variety of energy storage devices to retain the heat absorbed during the day so that it can be released during the night. Suppose that you were to use a device of this kind to produce steam at 100°C during the day, and then allow the steam to cool to 0°C and freeze during the night. How many kilograms of water would be needed to store 20.0 kWh of energy in this way? The latent heat of vaporization of water is 22.6 × 10⁵ J/kg, the latent heat of fusion of water is 33.5 × 10⁴ J/kg, and the specific heat capacity of water is 4186 J/kg ∙ K.

The temperature of an ideal gas in a sealed rigid 0.60- $m ^ { 3 }$ container is reduced from 460 K to $270 \mathrm {~K}$ The final pressure of the gas is $90 \mathrm { kPA } .$ The molar heat capacity at constant volume of the gas is 28.0 J/mol ∙ K. How much heat is absorbed by the gas during this process? (R = 8.31 J/mol ∙ K)

The density of water at 0°C is 999.84 kg/m³ and at 4°C it is 999.96 kg/m³. A 1.0-L container, full to the brim with water at 4.0°C is placed in the refrigerator. By the time that the temperature of the water reaches 0.0°C, what volume of water has spilled from the container, assuming that the contraction of the container is negligible?

A compression at a constant pressure of 200 kPa is performed on 8.00 moles of an ideal monatomic gas. The compression reduces the volume of the gas from $0.200 \mathrm {~m} ^ { 3 }$ to $0.120 \mathrm {~m} ^ { 3 }$ How much work was done by the gas during this process?

The process shown on the pV diagram in the figure is an

A glass flask has a volume of 500 mL at a temperature of 20° C. The flask contains 492 mL of mercury at an equilibrium temperature of 20°C. The temperature is raised until the mercury reaches the 500 mL reference mark. At what temperature does this occur? The coefficients of volume expansion of mercury and glass are 18 ×10^-5 K^-1 (mercury) and 2.0 ×10^-5 K^-1 (glass).

A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas of 0.0020 m². The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A. The end of the rod in alloy A is maintained at a temperature of 10°C, and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be 40° C, and the rate of heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy B?

An aluminum electric tea kettle with a mass of 500 g is heated with a 500-W heating coil. How long will it take to heat up 1.0 kg of water from 18°C to 98°C in the tea kettle? The specific heat of aluminum is 900 J/kg ∙ K and that of water is 4186 J/kg ∙ K.

A gas expands from an initial volume of 30.0 L to a final volume of 65.0 L at a constant pressure of 110 kPa. How much work is done by the gas during this expansion?

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