Exam 16: Sound and Hearing

Ideal gas law: Which contains more moles of material: 80 grams of helium gas (He, having atomic weight 4.0 g/mol) or 400 grams of argon gas (Ar, having atomic weight 40 g/mol)?

Quantity of heat: It is necessary to determine the specific heat of an unknown object. The mass of the object is measured to be 199.0 g. It is determined experimentally that it takes 16.0 J to raise the temperature 10.0°C. Find the specific heat of the object.

Phase changes: A chunk of ice (T = -20°C) is added to a thermally insulated container of cold water (T = 0°C). What happens in the container?

Phase changes: If you add 700 kJ of heat to 700 g of water at 70.0°C, how much water is left in the container? The latent heat of vaporization of water is 2.26 × J/kg and its specific heat is 4190 J/(kg ∙ K).

Mean free path: Assuming the radius of diatomic molecules is approximately for what pressure will the mean free path in room-temperature (20°C) nitrogen be 4.6 m? The Boltzmann constant is 1.38 × 10^-23 J/K, Avogadro's number is 6.02 × 10²³ molecules/mole, and the ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.

Thermal expansion: 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.)

Ideal gas law: A cold trap is set up to cause molecules to linger near the suction in a vacuum system. If the cold trap has an effective volume of 0.200 L and is maintained at how many molecules are in it at 10.0 Pa of pressure? (Avogadro's number is 6.022 × 10²³ molecules/mol, and the universal gas constant is 8.314 J/mol ∙ K. Assume the behavior of an ideal gas.)

Phase changes: A 406.0 kg copper bar is put into a smelter for melting. The initial temperature of the copper is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is 386 J/kg ∙ K, the heat of fusion for copper is 205 kJ/kg, and its melting point is 1357 K.)

Calorimetry: A block of ice at 0.000°C is added to a well-insulated 147-g aluminum calorimeter cup that holds 200 g of water at 10.0°C. The water and aluminum cup are in thermal equilibrium, and the specific heat of aluminum is 910 J/(kg ∙ K). If all but 2.00 g of ice melt, what was the original mass of the block of ice? The specific heat of water is 4190 J/(kg ∙ K), its latent heat of fusion is 334 kJ/kg, and its latent heat of vaporization is 2260 kJ/kg.

Conduction of heat: 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

Molecular speeds: If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that

Radiation: 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.

Mean free path: An ideal gas is kept in a rigid container. When its temperature is 100 K, the mean-free-path of the gas molecules is λ. What will be the mean-free-path of the molecules at 400 K?

Phase changes: A substance has a melting point of 20°C and a heat of fusion of 3.9 × J/kg. The boiling point is and the heat of vaporization is at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg ∙ K), 1000 J/(kg∙K), and 400 J/(kg ∙ K), respectively. The quantity of heat required to raise the temperature of of the substance from to at a pressure of 1.0 atm, is closest to

Quantity of heat: A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper; the aluminum and the copper are in thermal contact. The specific heat of aluminum is more than double that of copper. Which object experiences the greater temperature change during the time the system takes to reach thermal equilibrium?

Molecular speeds: If we double the root-mean-square speed (thermal speed) of the molecules of a gas, then

Thermal expansion: The coefficient of volume expansion of olive oil is 0.68 × 10^-3 K^-1. A 1.00-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 spill over the top of the beaker. What is the coefficient of linear expansion of the glass?

Ideal gas law: A bag of potato chips contains 2.00 L of air when it is sealed at sea level at a pressure of 1.00 atm and a temperature of 20.0°C. What will be the volume of the air in the bag if you take it with you, still sealed, to the mountains where the temperature is 7.00°C and atmospheric pressure is 70.0 kPa? Assume that the bag behaves like a balloon and that the air in the bag is in thermal equilibrium with the outside air. (1 atm = 1.01 × 10⁵ Pa)

Ideal gas law: A 25-L container holds ideal hydrogen (H₂) gas at a gauge pressure of 0.25 atm and a temperature of 0°C. What mass of hydrogen gas is in this container? The ATOMIC mass of hydrogen is 1.0 g/mol, the ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and 1.00 atm = 101 kPa.

Conduction of heat: A cylindrical bar that is 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