Chapter 18: A Macroscopic Description of Matter

A diving bell is a $3.0-m$-tall cylinder closed at the upper end but open at the lower end. The temperature of the air in the bell is $20°C$. The bell is lowered into the ocean until its lower end is $100m$deep. The temperature at that depth is $10°C$.

a. How high does the water rise in the bell after enough time has passed for the air inside to reach thermal equilibrium?

b. A compressed-air hose from the surface is used to expel all the water from the bell. What minimum air pressure is needed to do this?

An electric generating plant boils water to produce high-pressure steam. The steam spins a turbine that is connected to the generator.

a. How many liters of water must be boiled to fill a 5.0 m3 boiler with 50 atm of steam at 400$°$C?

b. The steam has dropped to 2.0 atm pressure at 150$°$C as it exits the turbine. How much volume does it now occupy?

The air temperature and pressure in a laboratory are 20$°$C and 1.0 atm. A 1.0 L container is open to the air. The container is then sealed and placed in a bath of boiling water. After reaching thermal equilibrium, the container is opened. How many moles of air escape?

$10,000{\mathrm{cm}}^3$of $200°\mathrm{C}$steam at a pressure of $20\mathrm{atm}$is cooled until it condenses. What is the volume of liquid water? Give your answer in ${\mathrm{cm}}^3$.

The mercury manometer shown in FIGURE P18.56 is attached

to a gas cell. The mercury height h is 120 mm when the cell is

placed in an ice-water mixture. The mercury height drops to

30 mm when the device is carried into an industrial freezer.

What is the freezer temperature?

Hint: The right tube of the manometer is much narrower than the

left tube. What reasonable assumption can you make about the gas

volume?

The U-shaped tube in FIGURE P18.57 has a total length of $1.0m$. It is open at one end, closed at the other, and is initially filled with air at $20°C\mathrm{and}1.0atm$pressure.

Mercury is poured slowly into the open end without letting any air escape, thus compressing the air. This is continued until the open side of the tube is completely filled with mercury. What is the length $L$of the column of mercury?

The $50kg$ circular piston shown in FIGURE P18.58 floats on $0.12mol$of compressed air.

a. What is the piston height $h$if the temperature is $30°C$?

b. How far does the piston move if the temperature is increased by $100°C$?

How many atoms are in a 2.0 cm * 2.0 cm * 2.0 cm cube of

aluminum?

A gas is in a Sealed container. The pressure is tripled and the temperature is doubled.

a. does the number of molecules within the container increase. decrease or stay the same?

b. By what factor does the number density of the gas increases.

An aquanaut lives in an underwater apartment 100 m beneath the surface of the ocean. Compare the freezing and boiling points of water in the aquanaut’s apartment to their values at the surface. Are they higher, lower, or the same? Explain.