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- 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? (b) If the diver breathes a gas mixture at a pressure of 1.50 ✕ 106 N/m2, what percent oxygen should it be to have the same oxygen partial pressure as at sea level?A mass m of helium gas is contained in a container of constant volume V, with a pressure P and absolute (Kelvin) temperature T at the start. More helium is added, increasing the total mass of helium gas to 3 m. The temperature is found to be 2T after this addition. In terms of the initial pressure P, what is the final gas pressure?Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A. The average translational kinetic energy per molecule in container B is?
- A hot air balloon uses the principle of buoyancy to create lift. By making the air inside the balloon less dense then the surrounding air, the balloon is able to lift objects many times its own weight. A large hot air balloon has a maximum balloon volume of 2090 m3 a. What is the density of air inside the balloon, in terms of the pressure P, temperature T, molar mass M, and the gas constant R? b. How much mass can this balloon lift (in addition to the mass of the gas inside) in terms the balloon volume Vb, the atmosphere air density ρa, the density of the air in the balloon ρg, and the gravitational acceleration g? c. If the air temperature in the balloon is 54 °C, how much additional mass, in kilograms, can the balloon lift? Assume the molar mass of air is 28.97 g/mol, the air density is 1.20 kg/m3, and the air pressure is 1 atm.2.97 moles of an ideal gas are placed in a container whose volume is 8.35 x10−3 m3. The absolute pressure of the gas is 7.2 x105 Pa. What is the average translational kinetic energy of a molecule of the gas?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.
- What is the RMS speed (in m/s) of a gas molecule, with mass 4.3x10-26 kg at a temperature of 98 degrees Fahrenheit?The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 9.0 atm and is increasing at a rate of 0.15 atm/min and V = 13 L and is decreasing at a rate of 0.17 L/min. Find the rate of change of T with respect to time at that instant if n = 10 mol. (Round your answer to four decimal places.) K/min dT_ dtThe spherical gas tank is fabricated by bolting together two hemispherical thin shells of thickness 30 mm. The gas contained in the tank is under a gauge pressure of 2.5 MPa. If the tank has an inner diameter of 8 m and is sealed with 900 bolts each 20 mm in diameter, determine the internal force carried by each bolt.
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