21. Kinetic Theory of Ideal Gases

A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. What is the reading of a pressure gauge attached to the tank?

A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. What is the number density of the oxygen?

A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if the Celsius temperature is doubled?

The interior of a Boeing 737-800 can be modeled as a 32-m-long, 3.7-m-diameter cylinder. The air inside, at cruising altitude, is 20°C at a pressure of 82 kPa. What volume of outside air, at −40°C and a pressure of 23 kPa, must be drawn in, heated, and compressed to fill the plane?

The 50 kg circular piston shown in FIGURE P18.57 floats on 0.12 mol of compressed air. What is the piston height h if the temperature is 30°C?

The 50 kg circular piston shown in FIGURE P18.57 floats on 0.12 mol of compressed air. How far does the piston move if the temperature is increased by 100°C?

The cylinder in FIGURE CP18.73 has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm², it contains 0.0040 mol of gas, and the spring constant is 1500 N/m. At 20°C the spring is neither compressed nor stretched. How far is the spring compressed if the gas temperature is raised to 100°C?

The closed cylinder of FIGURE CP18.74 has a tight-fitting but frictionless piston of mass M. The piston is in equilibrium when the left chamber has pressure p₀ and length L₀ while the spring on the right is compressed by ΔL. Suppose the piston is moved a small distance x to the right. Find an expression for the net force (Fₓ)_net on the piston. Assume all motions are slow enough for the gas to remain at the same temperature as its surroundings.

On average, each person in the industrialized world is responsible for the emission of 10,000 kg of carbon dioxide (CO₂) every year. This includes CO₂ that you generate directly, by burning fossil fuels to operate your car or your furnace, as well as CO₂ generated on your behalf by electric generating stations and manufacturing plants. CO₂ is a greenhouse gas that contributes to global warming. If you were to store your yearly CO₂ emissions in a cube at STP, how long would each edge of the cube be?

The 3.0-m-long pipe in FIGURE P18.49 is closed at the top end. It is slowly pushed straight down into the water until the top end of the pipe is level with the water's surface. What is the length L of the trapped volume of air?

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 100 m deep. The temperature at that depth is 10°C. How high does the water rise in the bell after enough time has passed for the air inside to reach thermal equilibrium?

An electric generating plant boils water to produce high-pressure steam. The steam spins a turbine that is connected to the generator. How many liters of water must be boiled to fill a 5.0 m³ boiler with 50 atm of steam at 400°C?

On a cool morning, when the temperature is 15°C, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is 45°C . What pressure will your tire gauge now show?

A 10-cm-diameter, 40-cm-tall gas cylinder, sealed at the top by a frictionless 50 kg piston, is surrounded by a bath of 20°C water. Then 50 kg of sand is slowly poured onto the top of the piston, where it stays. Afterward, what is the height of the piston?

A 6.0-cm-diameter cylinder of nitrogen gas has a 4.0-cm-thick movable copper piston. The cylinder is oriented vertically, as shown in FIGURE P19.49, and the air above the piston is evacuated. When the gas temperature is 20°C, the piston floats 20 cm above the bottom of the cylinder. What is the gas pressure?