Calculate the kinetic energy of helium molecules in 1 cm³ at pressure 2 atmosphere. (1 atmosphere = 1.013 x 10³ N/m²)
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Q: Ex. 13: Calculate the number of molecules in one liter of gas at N.T.P., if mass of each molecules…
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Q: Write the ideal gas law in terms of the mass density 17.1 (measured in kg/m³) of the gas. At 0 °C…
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Q: Ex. 13: Calculate the number of molecules in one liter of gas at N.T.P., if mass of each molecules…
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Q: at what pressure the mean square speed of a certain gas of density 1.2kg/m3 will be 2×105m/s?
A: Given data: The density of the gas is ρ=1.2 kg/m3. The arms speed is vrms=2×105 m/s.
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A: Partial pressure of oxygen is (20.9/100)*1.01*105 N/m2 = 2.12*104 N/m2
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- A sealed container has a volume of 0.012 m3 and contains 26.5 g of molecular nitrogen (N2), which has a molecular mass of 28.0 u. The gas is at 157 °C. What is the absolute pressure of the nitrogen gas, in kilopascals? 1 u = 1.67 x 10-27 kg.Problem 3: Consider a stationary horizontal slab of air of height dz. Since the slab is at rest, the pressure p holding it up from below must be balanced by the pressure from above PLUS the weight of the slab. a) Derive a formula for dP/dz the variation of pressure with altitude, in terms of the mass density p (greek letter rho) of the air. b) Using the ideal gas law, rewrite the air density in terms of the average mass m of the air molecules and other variables. Combine your result with part (a) to derive a differential equation relating dP/dz to P. Show then that pressure obeys the differential equation: dP тg dz kT c) Assume constant temperature T and solve the differential equation in part (b) for pressure P as a function of height z. Assume that P(z=0) is given. Show that the pressure obeys: P = P(0)e-mgz /kT Show also that the density obeys a similar equation.A vessel contains an ideal gas with temperature of -15°C, a density of 0.16 kg/m3, and a molecular weight of 4 g/mol. A) What is the pressure of this gas in kPa? B) Its gage pressure? C) If the vessel were punctured which way would gas flow - gas exiting the hole or atmosphere entering the hole? (Ri = 8.314 kg-m2/K-mol-s?)
- On Mars, the atmosphere is composed mainly of carbon dioxide. The value of the gas constant for the Martian atmosphere is 192 J/kg-K, and the acceleration of gravity there is 3.72 m/s?. At the average level of the Martian surface, the average temperature is 230 K, the pressure is 790 N/m?. At a certain altitude, the pressure is 680 N/m? and the average temperature is 203 K. 6. The temperature lapse rate is: A) – 0.01613 K/m B) – 0.1613 K/m C) – 1.613 K/m D) None of the above 7. The altitude is: A) 1200 m B) 1675 m C) 1765 m D) None of the above2.97 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?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_ dt
- When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV14 = C where C is a constant. Suppose that at a certain instant the volume is 560 cubic centimeters and the pressure is 81 kPa and is decreasing at a rate of 9 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? cm min (Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals. )An ideal gas is at a pressure 1.00 x 105 N/m2 and occupies a volume 20.00 m3. If the pressure of the gas is changed to 4 times its initial pressure while the temperature remains constant, what will be the new volume of the gas in m3?A basketball is pressurized to a gauge pressure of PG = 55 kPa when at the surface of a swimming pool. (Patm = 101 kPa). The ball is then submerged in the pool of water which has a density ρ = 1000 kg/m3. Assume the ball does not change in mass, temperature, or volume as it is submerged. Calculate the absolute pressure inside the basketball in kPa when it is at the surface. Write an equation for the pressure difference ΔP between the inside and outside of the ball when it is submerged a distance y below the surface of the water. Solve the pressure equation for the depth (in meters) at which the pressure difference between the inside and outside of the ball will become zero. At this depth the pressure inside the basketball is the same as the pressure outside the ball.
- Large helium-filled balloons are used to lift scientific equipment to high altitudes. What is the pressure inside such a balloon (in atm) if it starts out at sea level with a temperature of 20.8°C and rises to an altitude where its volume is sixteen times the original volume and its temperature is −35.7°C? (Enter your answer to at least 3 decimal places) What is the gauge pressure? (Enter your answer in atm and to at least 3 decimal places. Assume atmospheric pressure is constant.)An oxygen tank has a volume of 100 ft3. When one pound of gas is expelled from the tank, the temperature drops from 80°F to 60°F while the pressure drops to 100psig. Assuming that the oxygen acts as an ideal gas, what is the pressure reading (psig) in the pressure gauge initially?I put air in the tires of my car during the summer, while it was 28.8 °C outside (about 83.8 °F). My tires say to fill them to a pressure of 203,000 Pa. Boltzmann's constant is 1.38 * 10 ^ - 23 * J / K A) If my tires have a volume of 0.0100 m³, how many air molecules are in the tire? N = molecules B) These tires go all summer without losing any air, however come fall the temperature drops down to 8.65 °C (about 47.6 °F). Assuming the volume doesn't change (because it doesn't) what is the new pressure in my tires? P=