BackA helium balloon has volume V0 and temperature T0 at sea level where the pressure is P0 and the air density is ρ0. The balloon is allowed to float up in the air to altitude y where the temperature is T1. Show that the volume occupied by the balloon is then where .
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. Show the process on a pV diagram. Include a proper scale on both axes.
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?
The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10-10 mm of Hg. At T=20°C, how many molecules are in a cylindrical chamber 40 cm in diameter and 30 cm tall?
From the van der Waals equation of state, show that the critical temperature and pressure are given by Tcr = 8a / 27bR , Pcr = a / 27b². [Hint: Use the fact that the P versus V curve has an inflection point at the critical point so that the first and second derivatives are zero.]
Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H₂). The number density is about 1 atom/cm³ and the temperature is about 3 K. Estimate the pressure in interstellar space. Give your answer in Pa and in atm.
If a scuba diver fills his lungs to full capacity of 4.8 L when 9.0 m below the surface of sea water, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?
A gas at 100°C fills volume V0. If the pressure is held constant, what is the volume if the Celsius temperature is doubled?
Modern vacuum pumps make it easy to attain pressures of the order of atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. At a pressure of atm and an ordinary temperature of K, how many molecules are present in a volume of cm3?
A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. How many moles of gas are there?
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?
A balloon contains 3900cm3 of a gas at a pressure of 101 kPa and a temperature of –9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.
A 6.0-cm-diameter, 10-cm-long cylinder contains 100 mg of oxygen (O₂) at a pressure less than 1 atm. The cap on one end of the cylinder is held in place only by the pressure of the air. One day when the atmospheric pressure is 100 kPa, it takes a 184 N force to pull the cap off. What is the temperature of the gas?