Exam 12: Thermal Properties of Matter

What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C? The Boltzmann constant is 1.38 × 10^-23 J/K.

A certain ideal gas has a molar specific heat at constant pressure of 7R/2. What is its molar specific heat at constant volume?

A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow through the wall by 90 percent. The inner surface of the wooden wall is maintained at -10°C and the outer surface of the concrete wall is at 20°C. The thermal conductivities of concrete and wood are 0.80 W/m ∙ K (concrete) and 0.040 W/m ∙ K (wood). What should be the thickness of the layer of wood?

A sphere of surface area 1.25 m² and emissivity 1.0 is at a temperature of 100°C. At what rate does it radiate heat into empty space? (σ = 5.67 × 10^-8 W/m² ∙ K⁴)

The coefficient of linear expansion of copper is 17 × 10^-6 K^-1 and that of steel is 12 × 10^-6 K^-1. At 12°C a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm. Which one of the following quantities is closest to the temperature to which the copper pipe must be heated in order for the unheated steel rod to fit snugly in the copper pipe?

The coefficient of volume expansion of a certain olive oil is 0.68 × 10^-3 K^-1. A 1.0-L glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by 25 C°. As a result, 0.0167 L of olive oil spills over the top of the beaker. Which of the following values is closest to the coefficient of linear expansion of the glass from which the beaker is made?

A 45.0-kg sample of ice is at 0.00° C. How much heat is needed to melt it? For water L_F = 334,000 J/kg and L_V = 2.256 × 10⁶ J/kg.

A sealed 87- $m ^ { 3 }$ tank is filled with 6000 moles of ideal oxygen gas O₂ at an initial temperature of 270 K. The gas is heated to a final temperature of 460 K. The atomic mass of oxygen is 16.0 g/mol. How much heat is transferred to the gas during this process? (R = 8.31 J/mol ∙ K)

Two experimental runs are performed to determine the calorimetric properties of an alcohol which 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°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 capacity of water is 4190 J/kg ∙ K. Assume no heat is exchanged with the styrofoam container and the surroundings. What is the specific heat capacity of the alcohol?

A quantity of an ideal gas is kept in a rigid container of constant volume. If the gas is originally at a temperature of 19°C, at what temperature will the pressure of the gas double from its original value?

When a gas expands adiabatically,

A flask contains a mixture of argon and neon gases at a stabilized temperature. The root-mean-square speed of the argon gas is determined to be 1.21 km/s. What is the root-mean-square speed of the neon gas? The atomic mass of argon is 39.95 g/mol, and that of neon is 20.18 g/mol.

A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of 0° C. The rods are placed in line with a gap of 1.2 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 equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are 2.0 ×10^-5 K^-1 (brass) and 2.4 × 10^-5 K^-1 (aluminum).

A solid object has a volume density ρ₀ at a temperature of 315 K. The coefficient of volume expansion for the material of which it is made is 7.00 × 10^-5 K^-1. What will be its density (in terms of ρ₀ at a temperature of 425 K, assuming that it does not melt and that its thermal properties do not change with temperature?

Two identical objects are placed in a room with a temperature of 20°C. Object A has a temperature of 50°C, while object B has a temperature of 90°C. What is the ratio of the net power emitted by object B to the power emitted by object A?

The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and the other brass) of the same length and cross-sectional area are joined together end to end. The free end of the brass rod is maintained at 0°C and the free end of the aluminum rod is maintained at 200°C. If no heat escapes from the sides of the rods, what is the temperature at the place where the two rods are joined together?

A 5.00-g lead BB moving at 44.0 m/s penetrates a wood block and comes to rest inside the block. If half of its kinetic energy is absorbed by the BB, what is the change in the temperature of the BB? The specific heat of lead is 128 J/kg ∙ K.

At what temperature is the rms speed of hydrogen molecules, H₂, which have a molecular weight of 2.02 g/mole, equal to 2.0 km/s? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of 15°C. Both rods have the same diameter. The rods are now joined end-to-end to form a rod 90.0 cm long. If the temperature is now raised from 15°C to 90°C, what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is 2.4 × 10^-5 K^-1 and that of steel is 1.2 × 10^-5 K^-1.

Two metal rods are to be used to conduct heat from a region at 100°C to a region at 0°C as shown in the figure. The rods can be placed in parallel, as shown on the left, or in series, as on the right. When steady state flow is established, the heat conducted in the series arrangement is