A gas is in a container of volume V0 at pressure P0. It is being pumped out of the container by a piston pump. Each stroke of the piston removes a volume Vs through valve A and then pushes the air out through valve B as shown in Figure P19.74. Derive an expression that relates the pressure Pn of the remaining gas to the number of strokes n that have been applied to the container. FIGURE P19.74

The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25 degrees C, the pressure gage reads 205 kPa. If the volume of the tire is 0.021 m³, determine the amount of air that must be bled off to restore pressure to its original value if the air temperature in the tire rises to 38 degrees C. Assume the atmospheric pressure to be 100 kPa. The gas constant of air is R=0.287 kPa m³/(kg. K)

A frictionless piston of mass m = 3.0 kg is a precise fit in the narrow vertical cylindrical neck of a large container of volume V = 1000 litres and can move frictionless. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A = 1.00 x 10-4 m2. a) Assuming that the pressure and volume of the gas change slowly and isothermally, determine the differential equation of motion for small displacements of the piston about its equilibrium position and hence calculate the angular frequency of oscillation. [Hint: find an equilibrium pressure and consider how small displacement of the piston from the equilibrium position changes the volume and pressure in the vessel]. b) Without calculation, consider whether the frequency will increase or decrease if the pressure and volume of the gas were to change adiabatically. Explain your reasoning.

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.55 × 107 Pa and a temperature of 25.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (-78.5°C) to reduce the leak rate and pressure so that it can be safely repaired.           What is the final pressure, in pascals, in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change?  To what temperature, in kelvins, must the tank be cooled from its initial state to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)?

During inhalation, a person’s diaphragm and intercostal muscles contract, expanding the chest cavity and lowering the internal air pressure below ambient so that air flows in through the mouth and nose to the lungs. Suppose a person’s lungs hold 1250 mL of air at a pressure of 1.00 atm. If the person expands the chest cavity by 525 mL while keeping the nose and mouth closed so that no air is inhaled, what will be the air pressure in the lungs in atm? Assume the air temperature remains constant.

A deep sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of 1.01 ✕ 105 N/m2. (a) What is the partial pressure (in N/m2) of oxygen at sea level? N/m2 (b) If the diver breathes a gas mixture at a pressure of 2.00 ✕ 106 N/m2, what percent oxygen should it be to have the same oxygen partial pressure as at sea level? %

In the lungs, the respiratory membrane separates tiny sacs of air (absolute pressure=1.00x105 Pa) from the blood in the capillaries. These sacs are called alveoli, and it is from them that oxygen enters the blood. The average radius of the alveoli is 0.125 mm, and the air inside contains 14% oxygen, which is somewhat smaller amount than in fresh air. Assuming that the air behaves as an ideal gas at body temperature (310 K), find the number of oxygen molecules in one of the sacs.

Problem 10:  If you want to cook in water at 150°C, you need a pressure cooker that can withstand the necessary pressure. Part (a)  What pressure, in pascals, is required in the cooker for the boiling point of water to be that high? vapor pressure = 4.76 * 10( 5 ) Part (b)  If the lid of the pressure cooker is a disk 23.5 cm in diameter, what force, in newtons, must it be able to withstand at this pressure?