Exam 12: Thermal Properties of Matter

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. - How much total heat flows through the two rods each minute? The thermal conductivity of silver is 417 W/m ? K, and that of gold is 291 W/m ? 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 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.

A glass beaker of unknown mass contains $74.0 \mathrm { ml }$ of water. The system absorbs $2000.0 \mathrm { cal }$ of heat and the temperature rises $20.0 ^ { \circ } \mathrm { C }$ as a result. What is the mass of the beaker? The specific heat of glass is 0.18 cal/g ? °C, and that of water is 1.0 cal/g ? C°.

A 20.0-L pressure vessel holds 2.00 mol of oxygen at 30°C. What is the pressure inside the vessel? (R = 8.31 J/mol ∙ K)

If 50 g of lead (of specific heat 0.11 kcal/kg ∙ C°)at 100°C is put into 75 g of water (of specific heat 1.0 kcal/kg ∙ C°)at 0°C. What is the final temperature of the mixture?

A sample of an ideal gas is heated and its Kelvin temperature doubles. If the root-mean-square speed of its molecules was originally v, what is the new root-mean-square speed?

If we add 700 J of heat to 12 moles of an ideal monatomic gas at constant volume, what will be the change in temperature of the gas? (R = 8.31 J/mol ∙ K)

Consider two equal-volume flasks of gas at the same temperature and pressure. One gas, oxygen, has a molecular mass of 32. The other gas, nitrogen, has a molecular mass of 28. What is the ratio of the number of oxygen molecules to the number of nitrogen molecules in these flasks?

A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas of 0.0020 m². The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A. The end of the rod in alloy A is maintained at a temperature of 10°C, and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be 40° C, and the rate of heat flow in the rod is measured at 56 W. - What is the thermal conductivity of alloy A?

A 4.2-L flask of ideal neon gas (which is monatomic)is at a pressure of 3.3 atm and a temperature of 450 K. The atomic mass of neon is 20.2 g/mol. How many neon atoms are in the flask? (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa, N_A = 6.022 × 10²³ molecules/mol)

The water flowing over Niagara Falls drops a distance of 50 m. If all the gravitational potential energy is converted to thermal energy, by what temperature does the water rise? The specific heat of water is 4186 J/kg ∙ K.

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?

The figure shows a pV diagram for 0.0077 mol of ideal gas that undergoes the process 1 ? 2 ? 3. What is the volume V₃? (R = 8.31 J/mol ? K) the volume V₃?

At what temperature would the root-mean-square speed of hydrogen, H₂, molecules equal 11.2 km/s (the earth's escape speed)? The mass of a hydrogen atom is 1.67 × 10^-27 kg, and the Boltzmann constant is 1.38 × 10^-23 J/K.

If a certain sample of an ideal gas has a temperature of 104°C and exerts a pressure of 2.3 × 10⁴ Pa on the walls of its container, how many gas molecules are present in each cubic centimeter of volume? The ideal gas constant is R = 8.31 J/mol × K and Avogadro's number is N_A = 6.022 × 10²³ molecules/mol.

The volume coefficient of thermal expansion for gasoline is 950 × 10^-6 K^-1. By how many cubic centimeters does the volume of 1.00 L of gasoline change when the temperature rises from 30°C to 50°C?

A heat conducting rod, 1.60 m long and wrapped in insulation, is made of an aluminum section that is 0.90 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 $170 ^ { \circ } \mathrm { C }$ respectively. The thermal conductivities of aluminum and copper are 205 W/m ? K (aluminum)and 385 W/m ? K (copper). At what rate is heat conducted in the rod under steady state conditions?

A mercury thermometer has a glass bulb of interior volume 0.100 cm³ at 10°C. The glass capillary tube above the bulb has an inner cross-sectional area of 0.012 mm². The coefficient of volume expansion of mercury is 1.8 × 10^-4 K^-1. If the expansion of the glass is negligible, how much will the mercury rise in the capillary tube when the temperature rises from 5°C to 35°C if the bulb was full at 5°C?

If, with steady state heat flow established, you double the thickness of a wall built from solid uniform material, the rate of heat loss for a given temperature difference across the thickness will