Exam 19: Work, Heat, and the First Law of Thermodynamics

A compression, at a constant pressure of 190 kPa, is performed on 5.0 moles of an ideal monatomic gas. The compression reduces the volume of the gas from to The ideal gas constant is R = 8.314 J/mol ∙ K. The work done by the gas is closest to

How many grams of ice at -13°C must be added to 711 grams of water that is initially at a temperature of to produce water at a final temperature of Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is 4190 J/kg ∙ °C and of ice is 2050 J/kg · °C. For water the normal melting point is 0.00°C and the heat of fusion is 334 × 10³ J/kg. The normal boiling point is 100°C and the heat of vaporization is 2.26 × 10⁶ J/kg.

A heat conducting rod, 0.90 m long, is made of an aluminum section that is 0.10 m long, and a copper section that is long. Both sections have cross-sectional areas of The aluminum end is maintained at a temperature of and the copper end is at The thermal conductivity of aluminum is 205 W/m ∙ K and of copper is 385 W/m ∙ K. Steady state has been reached, and no heat is lost through the well-insulated sides of the rod. The temperature of the aluminum-copper junction in the rod is closest to

A copper cylinder with a mass of 125 g and temperature of 345°C is cooled by dropping it into a glass beaker containing 565 g of water initially at 20.0°C. The mass of the beaker is 50.0 g and the specific heat of the glass is 840 J/kg ∙ K. What is the final equilibrium temperature of the system, assuming the cooling takes place very quickly, so that no energy is lost to the air? The specific heat of copper is 385 J/kg ∙ K and that of water is 4190 J/kg ∙ K.

What is the net power that a person loses through radiation if her surface area is 1.20 m², if her emissivity is 0.895, if her skin temperature is 300 K, and if she is in a room that is at a temperature of 17°C? The Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴.

A substance has a melting point of 20°C and a heat of fusion of 3.5 × 10⁴ J/kg. The boiling point is 150°C and the heat of vaporization is 7.0 × 10⁴ J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg ∙ K), 1000 J/(kg ∙ K), and 400 J/(kg ∙ K), respectively. The quantity of heat given up by 0.50 kg of the substance when it is cooled from 170°C to 88°C, at a pressure of 1.0 atmosphere, is closest to

An ideal monatomic gas cools from 455.0 K to 405.0 K at constant volume as 831 J of energy is removed from it. How many moles of gas are in the sample? The ideal gas constant is R = 8.314 J/mol ∙ K.

A person makes ice tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many kilograms of ice, initially at 0.00°C, are required to bring the mixture to 10°C? The heat of fusion of ice is 334 kJ/kg, and we can assume that tea has essentially the same thermal properties as water, so its specific heat is 4190 J/(kg ∙ K).

A person pours 330 g of water at 45°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is 900 J/(kg ∙ K) and that of water is 4190 J/(kg ∙ K). What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

A cylinder contains 23 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.43 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol · K and the ideal gas constant is R = 8.314 J/mol ∙ K. The heat absorbed by the gas is closest to

During an isothermal process, 5.0 J of heat is removed from an ideal gas. How much work does the gas do during this process?

Two metal rods, one silver and the other copper, are both attached to a steam chamber as shown in the figure, with a temperature of 100°C, at one end, and an ice water bath, with a temperature of 0°C, at the other. The rods are 5.0 cm long and have a square cross-section, 2.0 cm on a side. When steady state has been reached, how much heat flows through the two rods in 1.0 min? The thermal conductivity of silver is 417 W/(m ∙ K), and that of copper is 395 W/(m ∙ K). No heat is exchanged between the rods and the surroundings, except at their ends.

A radiating body originally has a Kelvin temperature T_o, and its surroundings are at 500K (T_o > 500K). If the Kelvin temperature of the radiating body is increased to , the net rate at which the body radiates increases by a factor of 333. What was the original temperature ?

A monatomic ideal gas undergoes an isothermal expansion at 300 K, as the volume increased from to The final pressure is The ideal gas constant is R = 8.314 J/mol ∙ K. The heat transfer to the gas is closest to

An ideal gas initially at 300 K and occupying a volume of 20 L is adiabatically compressed. If its final temperature is 400 K and γ = 1.30, what is its final volume?

A chunk of ice (T = -20°C) is added to a thermally insulated container of cold water (T = 0°C). What happens in the container?

A heat conducting rod, 1.40 m long, is made of an aluminum section that is 0.50 m long and a copper section that is long. Both sections have cross-sectional areas of The aluminum end and the copper end are maintained at temperatures of and respectively. The thermal conductivity of aluminum is 205 W/m ∙ K of copper is 385 W/m ∙ K. The rate at which heat is conducted in the rod is closest to

When a fixed amount of ideal gas goes through an isothermal expansion,

A blacksmith is flattening a steel plate that measures 10 cm × 15 cm × 1 mm. He has heated the plate to 900 K. If the emissivity of the plate is 0.75, what is the total rate at which it radiates energy? The Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴. Ignore any heat it receives from the surroundings.

A system has a heat source supplying heat to an ideal gas at a rate of 187.0 W and the gas is doing work at a rate of 130.9 W. At what rate is the internal (thermal) energy of the gas changing?