Exam 12: Thermal Properties of Matter

A 6.5-g iron meteor hits the earth at a speed of 295 m/s. If its kinetic energy is entirely converted to heat in the meteor, by how much will its temperature rise? The specific heat of iron is 113 cal/kg ∙ C°, and 1 cal = 4.186 J.

An expansion process on an ideal diatomic ideal gas has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are: the pressure is 300 kPa, the volume is $0.0700 \mathrm {~m} ^ { 3 }$ and the temperature is $390 \mathrm {~K}$ The final pressure is $130 \mathrm { kPa }$ and the final temperature is $310 \mathrm {~K}$ How much work is done by the gas during this process? (R = 8.31 J/mol ∙ K)

A rigid container is filled with 4.0 mol of air with C_V = 2.5R. How much does the internal (thermal) energy of the air change if its temperature rises from $18 ^ { \circ } \mathrm { C }$ to $448 ^ { \circ } \mathrm { C } \text { ? }$ (R = 8.31 J/mol ∙ K)

A vertical cylinder, closed at the bottom end, contains 0.0100 mol of ideal gas. It is fitted at the top with a piston that can move freely. The mass of the piston is 14.0 kg and the initial height of the piston above the bottom of the cylinder is 25 cm. What is the temperature of the gas? (R = 8.31 J/mol ∙ 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?

For an ideal gas,

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 heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum section that is 0.20 m long and a copper section that is $0.70 \mathrm {~m}$ long. Both sections have a cross-sectional area of $0.00040 \mathrm {~m} ^ { 2 }$ The aluminum end and the copper end are maintained at temperatures of $30 ^ { \circ } \mathrm { C }$ and $230 ^ { \circ } \mathrm { C }$ respectively. The thermal conductivities of aluminum and copper are 205 W/m ∙ K (aluminum) and 385 W/m ∙ K (copper). What is the temperature of the aluminum-copper junction in the rod with steady state heat flow?

A 2294-kg sample of water at 0° C is cooled to $- 36 ^ { \circ } \mathrm { C }$ 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.

A 3.9-L volume of ideal neon gas (monatomic) is at a pressure of 5.6 aym and a temperature of $330 \mathrm {~K} \text {. }$ 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 $5.9 \text { L. }$ What is the final pressure of the gas?

What is the total translational kinetic energy of the gas in a classroom filled with nitrogen at $1.01 \times 10 ^ { 5 } \mathrm {~Pa}$ at $20.7 ^ { \circ } \mathrm { C } \text { ? }$ The dimensions of the classroom are $4.60 \mathrm {~m} \times 5.20 \mathrm {~m} \times 8.80 \mathrm {~m} .$ The Boltzmann constant is 1.3806503 × 10^-23 J/K, R = 8.31 J/mol ∙ K, and N_A = 6.022 × 10²³ molecules/mol.

Suppose that a rigid aluminum wire were to be strung out in a loop that just fits snugly around the equator (assuming a perfectly spherical Earth with a radius of 6.37 × 10⁶ m). If the temperature of the wire is increased by 0.50°C, and the increase in length is distributed equally over the entire length, how far off the ground will the wire loop be if it remained centered on the earth? The coefficient of linear expansion of aluminum is 24 × 10^-6 K^-1.

A certain ideal gas has a molar specific heat at constant pressure of 33.2 J/mol ∙ K. Its molar specific heat at constant volume is closest to which of the following values? (R = 8.31J/mol ∙ K)

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)

A balloon originally has a volume of 1.0 m³ when the gas in it is at 20°C and under a pressure of 1.0 atm. As it rises in the earth's atmosphere, its volume expands. What will be its new volume if its final temperature and pressure are -40°C and 0.10 atm?

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?

A sealed container holds 0.020 moles of ideal nitrogen (N₂) gas, at a pressure of 1.5 atm and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is 1.38 × 10^-23 J/K.

Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of -10.0° C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20.0°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20.0°C and the temperature at thermal equilibrium is 10.0°C. The specific heat capacity of water is 4190 J/kg ∙ K. Assume no heat is exchanged with the styrofoam container and the surroundings. What is the heat of fusion of the alcohol?

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).

A weather balloon containing 2.0 m³ of hydrogen gas rises from a location at which the temperature is 22°C and the pressure is 101 kPa to a location where the temperature is -39°C and the pressure is 20 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon?