Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 18, Problem 29P

The pressure gauge on a cylinder of gas registers the gauge pressure, which is the difference between the interior pressure and the exterior pressure P0. Let’s call the gauge pressure Pg. When the cylinder is full, the mass of the gas in it is mi at a gauge pressure of Pgi. Assuming the temperature of the cylinder remains constant, show that the mass of the gas remaining in the cylinder when the pressure reading is Pgf is given by

m f = m i ( P g f + P 0 P g i + P 0 )

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A cylinder of diameter S, of height h, contains pure gas with equation PV = nRT at constant temperature T_0. The z axis is directed upwards and the gravitational field is assumed to be uniform. 1) Using the fundamental principle of hydrostatic statistics, show that dp = -pgdz where p = p (z) is the gas pressure at height z. 2) If P_0 is the gas pressure at the foot of the pole, calculate the pressure p (z) at height z. 3) In the case of wind (M = 29 g / mol: R = 8.31J/ mol.k) at temperature T_0 = 300K, calculate the height of the poles necessary to observe the change in pressure (pressure at the threshold) at 5% .
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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

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