Exam 12: Thermal Properties of Matter

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?

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.

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.

A 5.00-g lead BB moving at 44.0 m/s penetrates a wood block and comes to rest inside the block. If half of its kinetic energy is absorbed by the BB, what is the change in the temperature of the BB? The specific heat of lead is 128 J/kg ∙ K.

A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water at 100°C and the other end in a water-ice mixture at 0°C. The rod has uniform cross-sectional area $7.05 \mathrm {~cm} ^ { 2 }$ and length $87 \mathrm {~cm} .$ The heat conducted by the rod melts the ice at a rate of 1.0 g every 11 seconds. What is the thermal conductivity of the rod? Recall that the heat of fusion of water is 3.34 × 10⁵ J/kg.

A 3.9-L volume of ideal neon gas (monatomic)is at a pressure of 5.6 aym and a temperature of $330 \mathrm {~K} .$ The atomic mass of neon is $20.2 \mathrm {~g} / \mathrm { mol }$ The temperature of the gas is now increased to 430 K and the volume is increased to $5.9 \mathrm {~L}$ What is the final pressure of the gas?

A 35-g block of ice at -14°C is dropped into a calorimeter (of negligible heat capacity)containing 400 g of water at 0°C. When the system reaches equilibrium, how much ice is left in the calorimeter? 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.

An 920-g piece of iron at 100°C is dropped into a calorimeter of negligible heat capacity containing 50 g of ice at 0°C and 92 g of water, also at 0°C. What is the final temperature of the system? The specific heat of iron is 448 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 substance has a melting point of 20°C and a heat of fusion of 3.4 × $10 ^ { 4 }$ J/kg. The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $6.8 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are 600 J/kg ? K (solid), 1000 J/kg ? K (liquid), and 400 J/kg ? K (gaseous). How much heat is required to raise the temperature of $1.90 \mathrm {~kg}$ of this substance from $- 4 ^ { \circ } \mathrm { C }$ to $106 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

A 0.50 $m ^ { 3 }$ gas tank holds 3.0 moles of ideal diatomic nitrogen gas at a temperature of $350 \mathrm {~K} .$ The atomic mass of nitrogen is $14.0 \mathrm {~g} / \mathrm { mol }$ . What is the rms speed of the molecules? (The Boltzmann constant is 1.38 × 10^-23 J/K, N_A = 6.022 × 10²³ molecules/mol.)

In an experiment to measure the thermal conductivity of a certain material, a slab of material 10.0 mm thick separates a steam chamber from a block of ice with a square cross-section with dimensions 8.00 cm × 8.00 cm. After 5.00 min of running the experiment, 64.0 g of ice have melted. What is the thermal conductivity of this material? The latent heat of fusion of water is 33.5 × 10⁴ J/kg, the latent heat of vaporization of water is 2.256 × 10⁶ J/kg, and both the ice and water are under 1.00 atm of pressure.

A 45.0-kg sample of ice is at 0.00° C. How much heat is needed to melt it? For water L_F = 334,000 J/kg and L_V = 2.256 × 10⁶ J/kg.

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

Two metal rods, one silver and the other gold, are attached to each other end-to-end. The free end of the silver rod is immersed in a steam chamber at 100°C, and the free end of the gold rod in an ice water bath at 0°C. The rods are both 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the ends. - What is the temperature at the point where the two rods are in contact with one another? The thermal conductivity of silver is 417 W/m ? K, and that of gold is 291 W/m ? K.

A certain ideal gas has a molar specific heat at constant volume 7R/2. What is its molar specific heat at constant pressure?

A 920-g empty iron kettle is put on a stove. How much heat in joules must it absorb to raise its temperature form $15.0 ^ { \circ } \mathrm { C }$ to $93.0 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat for iron is 113 cal/kg ? C°, and 1 cal = 4.186 J.

Solar houses use a variety of energy storage devices to retain the heat absorbed during the day so that it can be released during the night. Suppose that you were to use a device of this kind to produce steam at 100°C during the day, and then allow the steam to cool to 0°C and freeze during the night. How many kilograms of water would be needed to store 20.0 kWh of energy in this way? The latent heat of vaporization of water is 22.6 × 10⁵ J/kg, the latent heat of fusion of water is 33.5 × 10⁴ J/kg, and the specific heat capacity of water is 4186 J/kg ∙ K.

A 2294-kg sample of water at 0° C is cooled to $- 36 ^ { \circ } \mathrm { C } \text {, }$ and freezes in the process. How much heat is liberated? For water L_F = 334,000 J/kg and L_V = 2.256 × 10⁶ J/kg. The specific heat of ice is 2050 J/kg ? K.

The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and the other brass)of the same length and cross-sectional area are joined together end to end. The free end of the brass rod is maintained at 0°C and the free end of the aluminum rod is maintained at 200°C. If no heat escapes from the sides of the rods, what is the temperature at the place where the two rods are joined together?

How much heat is required to raise the temperature of 2.00 moles of an ideal monatomic gas by 10 C° at constant volume? (R = 8.31 J/mol ∙ K).