Exam 12: Thermal Properties of Matter

A 0.600-kg piece of metal X is heated to 100°C and placed in an aluminum can of mass 0.200-kg which contains 0.500 kg of water initially at 17.3°C. The final equilibrium temperature of the mixture is 20.2°C, what is the specific heat of metal X? The specific heats of water and aluminum are 4186 J/kg ∙ K (water) and 910 J/kg ∙ K (aluminum).

An ideal gas is held in a container of volume V at pressure p. The rms speed of a gas molecule under these conditions is v. If now the volume and pressure are changed to 2V and 2p, the rms speed of a molecule will be

A certain automobile tire has a volume of 0.0185 m³. If the absolute (or total) pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire? (R = 8.31 J/mol ∙ K, N_A = 6.022 x 10²³ molecules/mol)

In an electric furnace used for refining steel, the temperature is monitored by measuring the radiant power emitted through a small hole in the wall of the furnace, of area 0.5 cm². This hole acts like a perfect blackbody radiator having the same temperature as the interior of the furnace. If the temperature of the furnace (and therefore of the hole) is to be maintained at 1650°C, how much power will the hole radiate?

The absolute temperature of an ideal gas is directly proportional to which of the following quantities?

A person makes iced tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many kilograms of ice, initially at 0°C, are required to bring the mixture to 10°C? The specific heat of water (and tea) is 4186 J/kg ∙ K, and the latent heat of fusion of ice is 3.34 × 10⁵ J/kg.

How much heat must be added to a 8.0-kg block of ice at -8°C to change it to water at $14 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat of ice is 2050 J/kg ∙ C°, the specific heat of water is 4186 J/kg ∙ C°, the latent heat of fusion of ice is 334,000 J/kg, and 1 cal = 4.186 J.

Originally 2.00 mol of gas are at STP. If the temperature changes to 47.0°C and the pressure decreases to half of what it was, how many liters do the two moles now occupy? (1 atm = 101 kPa, R = 8.31 J/mol ∙ K)

(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?

When a sample of water at 0.0°C is cooled to -36.0°C and freezes in the process, 935,000 kJ of heat is liberated. What is the mass of this sample of water? For water L_F = 334,000 J/kg, L_V = 2.256 × 10⁶ J/kg, and the specific heat of ice is 2050 J/kg ∙ C°.

Which one of the following quantities is the smallest unit of heat energy?

A blacksmith is flattening a steel plate having dimensions 10 cm × 15 cm × 1 mm. He has heated the plate to 900 K. If the emissivity of the plate is 0.75, at what rate does it lose energy by radiation? Ignore any heat exchange with the surroundings. (σ = 5.67 × 10^-8 W/m² ∙ K⁴)

A 40.0-g block of ice at -15.00°C is dropped into a calorimeter (of negligible heat capacity) containing water at 15.00°C. When equilibrium is reached, the final temperature is 8.00°C. How much water did the calorimeter contain initially? The specific heat of ice is 2090 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.

A solid concrete wall has dimensions 4.0 m × 2.4 m and is 30 cm thick. The thermal conductivity of the concrete is 1.3 W/m ∙ K, and it separates a basement from the ground outside. The inner surface of the wall is at 18°C, and the outside surface is at 6°C. How much heat flows through the wall every hour?

The coefficient of linear expansion of steel is 12 × 10^-6 K^-1. What is the change in length of a 25-m steel bridge span when it undergoes a temperature change of 40 K from winter to summer?

The coefficient of linear expansion of copper is 17 × 10^-6 K^-1. A sheet of copper has a round hole with a radius of 3.0 m cut out of it. If the sheet is heated and undergoes a change in temperature of 80 K, what is the change in the radius of the hole?

How much heat must be removed from 456 g of water at 25.0°C to change it into ice at -10.0°C? The specific heat of ice is 2090 J/kg ∙ K, the latent heat of fusion of water is 33.5 × 10⁴ J/kg, and the specific heat of water is 4186 J/kg ∙ K.

An ideal gas undergoes the process a→b→c→a shown in the pV diagram. In this figure, P_a = P_c = 3.60 × 10⁵ Pa, V_b = V_c = 68.00 L, V_a = 35 L, and P_b = 5.60 × 10⁵ Pa. How much work is done by the system in this process?

A container of 114.0 g of water is heated using $67.0 \mathrm {~W}$ of power, with perfect efficiency. How long will it take to raise the temperature of the water from $15 ^ { \circ } \mathrm { C }$ to $25 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat capacity of the container is negligible, and the specific heat capacity of water is 4.186 × 10³ J/kg ∙ C.

When 50 g of a certain material at 100°C is mixed with 100 g of water at 0°C, the final temperature is 40°C. What is the specific heat of the material? The specific heat of water is 1.00 kcal/kg ∙ C°.