Advertisements
Advertisements
Question
A faulty barometer contains certain amount of air and saturated water vapour. It reads 74.0 cm when the atmospheric pressure is 76.0 cm of mercury and reads 72.10 cm when the atmospheric pressure is 74.0 cm of mercury. Saturation vapour pressure at the air temperature = 1.0 cm of mercury. Find the length of the barometer tube above the mercury level in the reservoir.
Advertisements
Solution
Given :
Let the CSA be A.
case 1 :
`V_1 = (x - 74) "A"`
SVP = 1 cm Hg
Atmospheric pressure, `"P"_0` = 76 cm Hg
Mercury column height = 74.0 cm
Let P be the air pressure above the barometer. Then,
Atmospheric pressure = SVP + Air pressure above the barometer mercury level + Mercury column height
⇒ 1+P+74 = 76
⇒ P = 1 cm
case 2 :
Atmospheric pressure, `"P"_0'` = 74.0 cm Hg
Let P' be the air pressure. Then,
`P^' + 72.10+1 = 76`
⇒ `P^' = 0.9`
`V_2 = (x - 72.1)A`
Applying Boyle's law, we get
`"PV"_1 = "P"^'"V"_2`
⇒ `1 xx (x - 74) A = 0.9 xx (x - 72.1)A`
⇒ x = 91.1 cm
Length of the tube = 91.1 cm
APPEARS IN
RELATED QUESTIONS
If it were possible for a gas in a container to reach the temperature 0 K, its pressure would be zero. Would the molecules not collide with the walls? Would they not transfer momentum to the walls?
A gas behaves more closely as an ideal gas at
Figure shows graphs of pressure vs density for an ideal gas at two temperatures T1 and T2.
The pressure of a gas kept in an isothermal container is 200 kPa. If half the gas is removed from it, the pressure will be
Equal masses of air are sealed in two vessels, one of volume V0 and the other of volume 2V0. If the first vessel is maintained at a temperature 300 K and the other at 600 K, find the ratio of the pressures in the two vessels.
Use R = 8.31 JK-1 mol-1
Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 20°C. During the day the temperature rises to 40°C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature.
A vessel contains 1.60 g of oxygen and 2.80 g of nitrogen. The temperature is maintained at 300 K and the volume of the vessel is 0.166 m3. Find the pressure of the mixture.
Use R = 8.3 J K-1 mol-1
Is a slow process always isothermal? Is a quick process always adiabatic?
In an adiabatic process on a gas with γ = 1.4, the pressure is increased by 0.5%. The volume decreases by about
A vessel of volume V0 contains an ideal gas at pressure p0 and temperature T. Gas is continuously pumped out of this vessel at a constant volume-rate dV/dt = r keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find (a) the pressure of the gas as a function of time, (b) the time taken before half the original gas is pumped out.
Use R = 8.3 J K−1 mol−1
Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at 0°C at a pressure of 76 cm of mercury. One of the bulbs is then placed in melting ice and the other is placed in a water bath maintained at 62°C. What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible.
A barometer tube is 80 cm long (above the mercury reservoir). It reads 76 cm on a particular day. A small amount of water is introduced in the tube and the reading drops to 75.4 cm. Find the relative humidity in the space above the mercury column if the saturation vapour pressure at the room temperature is 1.0 cm.
The human body has an average temperature of 98°F. Assume that the vapour pressure of the blood in the veins behaves like that of pure water. Find the minimum atmospheric pressure which is necessary to prevent the blood from boiling. Use figure for the vapour pressures.
On a winter day, the outside temperature is 0°C and relative humidity 40%. The air from outside comes into a room and is heated to 20°C. What is the relative humidity in the room? The saturation vapour pressure at 0°C is 4.6 mm of mercury and at 20°C it is 18 mm of mercury.
The temperature and the relative humidity are 300 K and 20% in a room of volume 50 m3. The floor is washed with water, 500 g of water sticking on the floor. Assuming no communication with the surrounding, find the relative humidity when the floor dries. The changes in temperature and pressure may be neglected. Saturation vapour pressure at 300 K = 3.3 kPa.
Use R = 8.31 J K-1 mol-1
If 1022 gas molecules each of mass 10-26 kg collide with a surface (perpendicular to it) elastically per second over an area of 1 m2 with a speed of 104 m/s, the pressure exerted by the gas molecules will be of the order of ______.
