Exam 12: Thermal Properties of Matter

(a)At what Celsius temperature is the average kinetic energy of a helium gas atom equal to 6.21 × 10^-21 J? The Boltzmann constant is 1.38 × 10^-23 J/K . (b)What would be the temperature for radon gas?

A 771.0-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 205,000 J/kg, and its melting point is 1357 K.

The melting point of aluminum is 660°C, its latent heat of fusion is 4.00 × 10⁵ J/kg, and its specific heat is 900J/kg ∙ K. How much heat must be added to 500 g of aluminum originally at 27°C to completely melt it?

The figure shows a pV diagram for 2.6 g of ideal helium gas that undergoes the process 1 → 2 → 3. Find the value of volume V₃. The atomic mass of helium is 4.0 g/mol, and R = 8.31 J/mol ∙ K.

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.

A 400-g block of iron at 400°C is dropped into a calorimeter (of negligible heat capacity)containing 60 g of water at 30°C. How much steam is produced? The latent heat of vaporization of water is 22.6 × 10⁵ J/kg and its specific heat capacity is 4186 J/kg ∙ K. The average specific heat of iron over this temperature range is 560 J/kg ∙ K.

For an ideal gas,

A runner generates 1260 W of thermal energy. If this heat has to be removed only by evaporation, how much water does this runner lose in 15 minutes of running? The latent heat of vaporization of water is 22.6 × 10⁵ J/kg.

An ideal gas is compressed isothermally to one-third of its initial volume. The resulting pressure will be

How many molecules are in (a)1.0 cm³ of air at STP and (b)1.0 cm³ of helium at STP? (R = 8.31 J/mol . K, N_A = 6.022 × 10²³ molecules/mol)

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

A 90-g aluminum calorimeter contains 390 g of water at an equilibrium temperature of $20 ^ { \circ } \mathrm { C }$ A $160 - g$ piece of metal, initially at $305 ^ { \circ } \mathrm { C } \text {, }$ is added to the calorimeter. The final temperature at equilibrium is 32° C. Assume there is no external heat exchange. The specific heat capacities of aluminum and water are 910 J/kg ? K (aluminum)and 4190 J/kg ? K (water). What is the specific heat capacity of the 160-g piece of metal?

A 400-g stainless steel 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 2.0 mm thick. At a certain moment, the temperature of the water is 75°C, and it is rising at the rate of 3.0 C° per minute. What is the difference in temperature between the inside and the outside of the bottom of the tea kettle? Assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of stainless steel is 16.3 W/m ∙ K, the specific heat of the steel is 448 J/kg ∙ K, and the specific heat of water is 4186 J/kg . K.

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.

A lab student drops a 400.0-g piece of metal at 120.0°C into a cup containing 450.0 g of water at 15.0°C. After waiting for a few minutes, the student measures that the final temperature of the system is 40.0°C. What is the specific heat of the metal, assuming that no significant heat is exchanged with the surroundings or the cup? The specific heat of water is 4186 J/kg ∙ K.

The figure shows a pV diagram for 0.0061 mol of ideal gas that undergoes the process 1 → 2 → 3. What is the pressure p₂? (R = 8.31 J/mol ∙ K)

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?

The melting point of aluminum is 660°C, its latent heat of fusion is 4.00 × 10⁵ J/kg, and its specific heat is 900 J/kg ∙ K. If 300 kJ of heat are added to 442 g of aluminum at 100°C, what is the final state of the system? That is, how much is liquid, how much is solid, and what is its temperature?

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. If they are heated together to a higher temperature, which one of the following quantities is closest to the common temperature at which the steel rod will fit snugly in the copper pipe?

The cylindrical filament in a light bulb has a diameter of 0.050 mm, an emissivity of 1.0, and a temperature of 3000°C. How long should the filament be in order to radiate 60 W of power? (σ = 5.67 × 10^-8 W/m² ∙ K⁴)