The ideal gas law can be recast in terms of the density of a gas. (a) Use dimensional analysis to find an expression for the density r of a gas in terms of the number of moles n, the volume V, and the molecular weight M in kilograms per mole. (b) With the expression found in part (a), show thatfor an ideal gas. (c) Find the density of the carbon dioxide atmosphere at the surface of Venus, where the pressure is 90.0 atm and the temperature is 7.00 x 102 K. (d) Would an evacuated steel shell of radius 1.00 m and mass 2.00 x 102 kg rise or fall in such an atmosphere? Why?

The ideal gas law can be recast in terms of the density of a gas. (a) Use dimensional analysis to find an expression for the density r of a gas in terms of the number of moles n, the volume V, and the molecular weight M in kilograms per mole. (b) With the expression found in part (a), show thatfor an ideal gas. (c) Find the density of the carbon dioxide atmosphere at the surface of Venus, where the pressure is 90.0 atm and the temperature is 7.00 x 102 K. (d) Would an evacuated steel shell of radius 1.00 m and mass 2.00 x 102 kg rise or fall in such an atmosphere? Why?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter15: Fluid Mechanics

Section: Chapter Questions

Problem 29P: How many cubic meters of helium are required to lift a balloon with a 400-kg payload to a height of...

See similar textbooks

Similar questions

Humans evolved in Earth's atmosphere, therefore the pressures interior to the body are relatively close to atmospheric pressure. Because the differences between internal body pressures and atmospheric pressure are so small, individuals have a difficult time gauging the magnitude of atmospheric pressure. Suppose an individual is lying on his stomach with sheets of paper stacked on his back. If each sheet of paper has a mass of 0.00280 kg and is the standard letter size of 8.5 in by 11 in (0.216 m by 0.279 m), how many sheets must be stacked to produce a pressure on his back equal to atmospheric pressure (roughly 101325 Pa)?
How many cubic meters of helium are required to lift a balloon with a 400-kg payload to a height of 8 000 m? Take He = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression air = 0ez/8, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.
An expression for buoyant force is FB = ρgV, where FB has dimensions [MLT−2], ρ (density) has dimensions [ML−3], and g (gravitational field strength) has dimensions [LT−2]. The correct interpretation of V is that it represents velocity or volume?
An expression for buoyant force is FB = ρgV, where FB has dimensions [MLT−2], ρ (density) has dimensions [ML−3], and g (gravitational field strength) has dimensions [LT−2]. What must be the dimensions of V? [M2] or [MLT−2] or [L3] or [MLT]? Does the interpreation of V represent volume or velocity?
Under standard conditions, the density of air is 1.29 kg/m3. What is the mass of the air inside a room measuring 4.0 m × 3.0 m × 2.0 m?
The density of a 2-cubic meter block of mass of 1000 kg is how much kg/m^3?
If the density (mass divided by volume) of the wall material is the same as that of pure water, what is the mass (in mgmg) of the cell wall, assuming the cell to be spherical and the wall to be a very thin spherical shell?
You are with an excursion party on an exploration of the surface of Mars. You find a small lake of water of that 1.76 m. Assume the density of the freshwater is unchanged on Mars. You measure the absolute pressure at the bottom of the lake to be one 161,800 Pa. What is the absolute pressure (in atm) at the surface of the lake. Assume the value of G on Mars is 3.72 m/s^2
Assuming the normal barometric pressure , how deep in the ocean is the point where an air bubble , upon reaching the surface , has six times its volume that it had at the bottom
While researching fluid dynamics, you come across a reference to the dimensionless number called the capillary number, given by the equation below. Ca=\frac{\mu v}{\gamma }, where mu = fluid viscosity [=] g/m s and v = velocity [=] ft/s what is gamma?
If the atmospheric pressure is 1,051 mm Hg and the height difference between the two arms is 14.4 cm , what is the pressure of the gas sample below in atmospheres (atm)?
Starting with an atmospheric pressure of 101,325 Pa, express the magnitude of the pressure in the following units: (a) millimeters of mercury (mm Hg), (b) centimeters of mercury (in Hg), and (c) meters of water . The densities of water and mercury are ρH2O = 1,000 kg⁄m3 and ρHg =13,550 kg⁄m3 respectively.