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. Sketch a PV diagram for the process. Take the density of water to be 1000 kg/m³.

A gas in a cylinder held at a constant pressure 1.80×10⁵ Pa expands from a volume of 1.2 m³ to 1.6 m³. The internal energy of the gas decreases from 4.40×10⁵ J to 3×10⁵ J. How much heat was transferred to the gas?

The internal energy of a system decreases by 500 J, and 230 J of work is done on the system. What is the heat transfer into or out of this system?

When water is boiled at a pressure of $2.00$ atm, the heat of vaporization is $2.20\times10^6$ J/kg and the boiling point is $120$°C. At this pressure, $1.00$ kg of water has a volume of $1.00\times10^{-3}$ 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 in a cylinder is held at a constant pressure of $1.80\times {10}^5$ Pa and is cooled and compressed from $1.70$ m³ to $1.20$ m³. The internal energy of the gas decreases by $1.40\times {10}^5$ J. Does it matter whether the gas is ideal? Why or why not?

Five moles of an ideal monatomic gas with an initial temperature of $127$°C expand and, in the process, absorb $1500$ J of heat and do $2100$ J of work. What is the final temperature of the gas?

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 gas in a cylinder expands from a volume of $0.110$ m³ to $0.320$ m³ . Heat flows into the gas just rapidly enough to keep the pressure constant at $1.65\times {10}^5$ Pa during the expansion. The total heat added is $1.15\times {10}^5$ J. Find the work done by the gas.

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.

(II) How many joules and kilocalories are generated when the brakes are used to bring a 1200-kg car to rest from a speed of 95 km/h?

(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?

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.