22. The First Law of Thermodynamics

A scuba diver releases a 3.60-cm-diameter (spherical) bubble of air from a depth of 14.0 m. Assume the temperature is constant at 298 K, and that the air behaves as an ideal gas. How large is the bubble when it reaches the surface? Take the density of water to be 1000 kg/m³.

(I) An ideal gas expands isothermally, performing 4.30 x 10³ J of work in the process. Calculate the change in internal energy of the gas, and

Which of the following statements best describes the first law of thermodynamics?

When water is boiled at a pressure of $2.00$ atm, the heat of vaporization is $2.20\(\times\)10^6$ J/kg and the boiling point is $120$°C. At this pressure, $1.00$ kg of water has a volume of $1.00\(\times\)10^{-3}$ m³, and $1.00$ kg of steam has a volume of $0.824$ m³. Compute the increase in internal energy of the water.

A gas cylinder holds 0.10 mol of O₂ at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the pressure is halved. What are the final volume?

Two cylinders each contain 0.10 mol of a diatomic gas at 300 K and a pressure of 3.0 atm. Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is 1.0 atm. What are the final temperature and volume of each?

(II) How much work is done by a pump to slowly compress, isothermally, 3.20 L of nitrogen at 0°C and 1.00 atm to 1.80 L at 0°C?

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is $27.0$°C and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done $2.40\times {10}^3$ J of work.

When water is boiled at a pressure of $2.00$ atm, the heat of vaporization is $2.20\times {10}^6$ J/kg and the boiling point is $120$°C. At this pressure, $1.00$ kg of water has a volume of $1.00\times {10}^{-3}$ m³, and $1.00$ kg of steam has a volume of $0.824$ m³. Compute the work done when $1.00$ kg of steam is formed at this temperature.

A scuba diver releases a 3.60-cm-diameter (spherical) bubble of air from a depth of 14.0 m. Assume the temperature is constant at 298 K, and that the air behaves as an ideal gas. Apply the first law of thermodynamics to the bubble, and find the work done by the air in rising to the surface, the change in its internal energy, and the heat added or removed from the air in the bubble as it rises. Take the density of water to be 1000 kg/m³.

(II) A 64-kg ice skater moving at 8.5 m/s glides to a stop. Assuming the ice is at 0°C and that 50% of the heat generated by friction is absorbed by the ice, how much ice melts?