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Chapter 9: Problem 23

When a mercury manometer is connected to a gas main, the mercury stands $40.0 \mathrm{cm}$ higher in the tube that is open to the air than in the tube connected to the gas main. A barometer at the same location reads $74.0 \mathrm{cm}\( Hg. Determine the absolute pressure of the gas in \)\mathrm{cm}$ Hg.

Short Answer

Expert verified
Answer: The absolute pressure of the gas is 114.0 cm Hg.

Step by step solution

01

Find the pressure difference using the mercury manometer reading

The mercury manometer reading tells us that the level of mercury is 40.0 cm higher in the tube open to the air than the one connected to the gas main. This difference in height corresponds to the pressure difference between the gas and the atmosphere. Since the height difference is given in cm, we don't need to convert the units. Therefore, the pressure difference is 40.0 cm Hg.
02

Find the atmospheric pressure using the barometer reading

We are given the barometric reading, which tells us the atmospheric pressure at the location. The barometer reads 74.0 cm Hg. This is the atmospheric pressure at that specific location.
03

Calculate the absolute pressure of the gas

Now that we have both the pressure difference between the gas and the atmosphere (40.0 cm Hg) and the atmospheric pressure (74.0 cm Hg), we can calculate the absolute pressure of the gas. To do this, we need to add the pressure difference to the atmospheric pressure: Absolute pressure of the gas = Atmospheric pressure + Pressure difference Absolute pressure of the gas = 74.0 cm Hg + 40.0 cm Hg
04

Write the final answer

Now, we just need to perform the final calculation to find the absolute pressure of the gas: Absolute pressure of the gas = 114.0 cm Hg So, the absolute pressure of the gas is 114.0 cm Hg.

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Most popular questions from this chapter

A bug from South America known as Rhodnius prolixus extracts the blood of animals. Suppose Rhodnius prolixus extracts \(0.30 \mathrm{cm}^{3}\) of blood in 25 min from a human arm through its feeding tube of length \(0.20 \mathrm{mm}\) and radius \(5.0 \mu \mathrm{m} .\) What is the absolute pressure at the bug's end of the feeding tube if the absolute pressure at the other end (in the human arm) is 105 kPa? Assume the viscosity of blood is 0.0013 Pa-s. [Note: Negative absolute pressures are possible in liquids in very slender tubes.]
A house with its own well has a pump in the basement with an output pipe of inner radius \(6.3 \mathrm{mm}\). Assume that the pump can maintain a gauge pressure of \(410 \mathrm{kPa}\) in the output pipe. A shower head on the second floor (6.7 \(\mathrm{m}\) above the pump's output pipe) has 36 holes, each of radius \(0.33 \mathrm{mm} .\) The shower is on "full blast" and no other faucet in the house is open. (a) Ignoring viscosity, with what speed does water leave the shower head? (b) With what speed does water move through the output pipe of the pump?
The average speed of blood in the aorta is \(0.3 \mathrm{m} / \mathrm{s}\) and the radius of the aorta is \(1 \mathrm{cm} .\) There are about \(2 \times 10^{9}\) capillaries with an average radius of \(6 \mu \mathrm{m}\). What is the approximate average speed of the blood flow in the capillaries?
An IV is connected to a patient's vein. The blood pressure in the vein has a gauge pressure of \(12 \mathrm{mm}\) Hg. At least how far above the vein must the IV bag be hung in order for fluid to flow into the vein? Assume the fluid in the IV has the same density as blood.
The diameter of a certain artery has decreased by \(25 \%\) due to arteriosclerosis. (a) If the same amount of blood flows through it per unit time as when it was unobstructed, by what percentage has the blood pressure difference between its ends increased? (b) If, instead, the pressure drop across the artery stays the same, by what factor does the blood flow rate through it decrease? (In reality we are likely to see a combination of some pressure increase with some reduction in flow.)
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