21. Kinetic Theory of Ideal Gases

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?

Helium gas with a volume of $3.20$ L, under a pressure of $0.180$ atm and at $41.0$°C, is warmed until both pressure and volume are doubled. What is the final temperature?

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?

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?

10 g of dry ice (solid CO₂) is placed in a 10,000 cm³ container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0°C, a temperature at which CO₂ is a gas. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is 1000 cm³.

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?

Assume that in an alternate universe, the laws of physics are very different from ours and that “ideal” gases behave as follows: At constant pressure, the volume varies directly with the 2/3 power of the temperature.

Assume that in an alternate universe, the laws of physics are very different from ours and that “ideal” gases behave as follows: At 273.15 K and 1.00 atm pressure, 1.00 mole of an ideal gas is found to occupy 22.4 L. Obtain the form of the ideal gas law in this alternate universe, including the value of the gas constant R.

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled. What is the gas temperature after the expansion (in °C)? The gas pressure is then decreased at constant volume until the original temperature is reached.

1.00 mole of an ideal monatomic gas at STP first undergoes an isothermal expansion so that the volume at b is 2.5 times the volume at a (Fig. 20–25). Next, heat is extracted at a constant volume so that the pressure drops. The gas is then compressed adiabatically back to the original state. Calculate the pressures at b and c.

In Problems $67, 68, 69,$ and $70$ you are given the equation(s) used to solve a problem. For each of these, you are to draw a pV diagram.

$(T_2 + 273) \(\text{ K}\) = \(\frac{200 \text{ kPa}\)}{500 \(\text{ kPa}\)} \(\times\) 1 \(\times\) (400 + 273) \(\text{ K}\)$

A heat engine takes a diatomic gas around the cycle shown in Fig. 20–23. Determine the temperature at point c.

A heat engine takes a diatomic gas around the cycle shown in Fig. 20–23. Using the ideal gas law, determine how many moles of gas are in this engine.

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 standard cylinder of oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and volume = 14L (0.014m³) at T = 295 K . How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.0 L/min?