Exam 12: Thermal Properties of Matter

Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B. If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures T_A and T_B in containers A and B, respectively, is

A car starts out when the air temperature is 288 K and the absolute (total)air pressure in the tires is 500 kPa. After driving a while, the temperature of the air in the tires increases to 298 K. What is the pressure in the tires at that point, assuming their volume does not change?

A 360-g metal container, insulated on the outside, holds 180.0 g of water in thermal equilibrium at 22.0°C. A 24.0-g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is 15.0°C. Assume there is no heat exchange with the surroundings. For water, the specific heat capacity is 4190 J/kg ∙ K and the heat of fusion is 3.34 × 10⁵ J/kg. What is the specific heat capacity of the metal of the container?

A sample of ideal monatomic gas is cooled by 50.0 C° at constant volume by removing 831 J of energy from it. How many moles of gas are in the sample? (R = 8.31 J/mol ∙ K)

An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 × 10^-6 K^-1.

A solid cylindrical bar conducts heat at a rate of 25 W from a hot to a cold reservoir under steady state conditions. If both the length and the diameter of this bar are doubled, the rate at which it will conduct heat between these reservoirs will be

An ideal gas has a pressure of 2.5 atm, a volume of 1.0 L at a temperature of 30°C. How many molecules are there in this gas? (R = 8.31 J/mol ∙ K,1.00 atm = 101 kPa, N_A = 6.022 × 10²³)

A 24.0-L tank contains ideal helium gas at 27°C and a pressure of 22.0 atm. How many moles of gas are in the tank? (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa)

Two processes are shown on the pV diagram in the figure. One of them is an adiabat and the other one is an isotherm. Which process is the isotherm?

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 gas expands from an initial volume of 30.0 L to a final volume of 65.0 L at a constant pressure of 110 kPa. How much work is done by the gas during this expansion?

A hole 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 K^-1.

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?

If the absolute temperature of an object is tripled, the thermal power radiated by this object (assuming that its emissivity and size are not affected by the temperature change)will

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?

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen molecules, compared to that of hydrogen molecules,

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 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)

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).

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?