Exam 12: Thermal Properties of Matter

A piece of iron of mass 0.12 kg is taken from an oven where its temperature is 336°C and quickly placed in an insulated copper can that contains 0.20 kg of water. The copper can has mass 0.50 kg, and it and the water in it are originally at a temperature of 20°C. Calculate the final temperature of the system, assuming no heat is lost to the surroundings. Use the following specific heats: 4190J/kg ∙ C° (water), 470 J/kg ∙ C° (iron), and 390 J/kg ∙ C° (copper).

An ideal gas occupies 6.00 × 10² cm³ at 20°C. At what temperature will it occupy 1.20 × 10³ cm³ if the pressure is held constant?

The molecular weight of nitrogen, N₂, is 28 g/mol. What is the rms speed of nitrogen molecules in a cooler at 8.0°C? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

A beaker of negligible heat capacity contains 456 g of ice at -25.0°C. A lab technician begins to supply heat to the container at the rate of 1000 J/min. How long after starting will it take before the temperature starts to rise above 0°C? The specific heat of ice is 2090 J/kg ∙ K and the latent heat of fusion of water is 33.5 × 10⁴ J/kg.

An architect is interested in estimating the rate of heat loss, ΔQ/Δt, through a sheet of insulating material as a function of the thickness of the sheet. Assuming fixed temperatures on the two faces of the sheet and steady state heat flow, which one of the graphs shown in the figure best represents the rate of heat transfer as a function of the thickness of the insulating sheet?

Object 1 has three times the specific heat capacity and four times the mass of Object 2. The two objects are given the same amount of heat. If the temperature of Object 1 changes by an amount ΔT, the change in temperature of Object 2 will be

A jar holds 2.0 L of ideal nitrogen gas, N₂, at STP. The atomic mass of nitrogen is 14.0 g/mol, the ideal gas constant is R = 8.31 J/mol ∙ K, Avogadro's number is N_A = 6.022 × 10²³ molecules/mol, and 1.00 atm = 101 kPa. (a) How many moles of nitrogen are in the jar? (b) How many nitrogen molecules are in the jar? (c) What is the mass of the nitrogen in the jar?

The root-mean-square speed of the molecules of an ideal gas is v. The gas is now slowly compressed to one-half its original volume with no change in temperature. What is the root-mean-square speed of the molecules now?

How many moles are there in 2.00 kg of copper? The atomic weight of copper is 63.5 g/mol and its density is 8.90 g/cm³.

In a given reversible process, the temperature of an ideal gas is kept constant as the gas is compressed to a smaller volume. Which one of the following statements about the gas is correct?

A steel bridge is 1000 m long at -20°C in winter. What is the change in length when the temperature rises to 40°C in summer? The average coefficient of linear expansion of this steel is 11 × 10^-6 K^-1.

A 0.40- $m ^ { 3 }$ gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of $290 \mathrm {~K}$ The atomic mass of nitrogen is $14.0 \mathrm {~g} / \mathrm { mol }$ . What is the pressure of the gas? (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa)

A sealed cylinder fitted with a movable piston contains ideal gas at 27°C, pressure 0.500 × 10⁵ Pa, and volume 1.25 m³. What will be the final temperature if the gas is compressed to 0.800 m³ and the pressure rises to 0.820 × 10⁵ Pa?

The figure shows a pV diagram for 2.9 g of ideal oxygen gas O₂ in a sealed container. The temperature of state 1 is 76° C, the atomic mass of the oxygen atom is 16 g/mol, and R = 8.31 J/mol ∙ K. What are the temperatures T₃ and T₄?

A laboratory vacuum pump can reduce the pressure in a chamber to 1.0 × 10^-7 Pa. If the volume of the chamber is 0.500 m³ and the temperature is 27°C, how many molecules are left inside the chamber? (N_A = 6.022 × 10²³ molecules/mol, R = 8.31 J/mol ∙ K)

A lab assistant drops a 400.0-g piece of metal at 100.0°C into a 100.0-g aluminum cup containing 500.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ In a few minutes, she measures the final temperature of the system to be 40.0°C. What is the specific heat of the 400.0-g piece of metal, assuming that no significant heat is exchanged with the surroundings? The specific heat of this aluminum is 900.0 J/kg ∙ K and that of water is 4186 J/kg ∙ K.

If 50 g of lead (of specific heat 0.11 kcal/kg ∙ C°) at 100°C is put into 75 g of water (of specific heat 1.0 kcal/kg ∙ C°) at 0°C. What is the final temperature of the mixture?

If you wanted to know how much the temperature of a particular piece of material would rise when a known amount of heat was added to it, which of the following quantities would be most helpful to know?

A glass tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of 0.090 m² and is 1.5 mm thick. At a certain moment, the temperature of the water is 75°C, and it is rising at the rate of 3 C° per minute. What is the temperature of the outside surface of the bottom of the tea kettle? Neglect the heat capacity of the kettle, and assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of glass is 0.840 W/m ∙ K and the specific heat of water is 4186 J/kg ∙ K.

If the temperature of a gas is increased from 20°C to 100°C, by what factor does the rms speed of an ideal molecule change?