A container of volume 50 cc contains air (mean molecular weight = 28.8 g) and is open to atmosphere where the pressure is 100 kPa. The container is kept in a bath containing melting ice (0°C).
(a) Find the mass of the air in the container when thermal equilibrium is reached.
(b) The container is now placed in another bath containing boiling water (100°C).
Find the mass of air in the container.
(c) The container is now closed and placed in the melting-ice bath. Find the pressure of the air when thermal equilibrium is reached.
Volume of container V1=50cc=5010-6m3
Molecular mass of air in container M= 28.8g
Pressure of air P1= 100kPa=105Pa
(a) We know ideal gas equation
Where V= volume of gas
n=number of moles of gas
P=pressure of gas
In first case the air is kept in container having ice. So, temperature in case will be T1 =0=273.15K
Number of moles n= …. (1)
Number of moles n= …. (2)
Equating (1) and (2) we get
So, mass of air when temperature is 0 is 0.0635g.
(b) Now in second case the container having air is kept in a bath having boiling water. So, temperature will be T2=100=373.15K.
Since, now temperature is 100 therefore, some of the air will be expelled as air will expand but the volume of container is fixed. So, some of the air will go out of the container as container is open.
So, first we will calculate the mass of air expelled from container and then we will subtract it from the original volume V1 to get the mass of remaining air.
Pressure will be same as before, as the air is still open to atmosphere. So P2=P1.
Let the volume of expanded gas be V2. Number of moles in volume V2 be the same as before because no extra gas is added. It has just expanded.
As P2=P1, therefore
Volume of gas expelled out the container
Number of moles of expelled gas
So, the mass of gas remaining in the container
So, the mass of gas when temperature is 100 is 0.0456g.
(c) Now the container is kept in ice bath i.e. temperature 0 and container is closed. So, now the pressure will change.
Number of moles left =
Applying ideal gas equation
Pressure of gas when lid is closed, and temperature is 0 is 73.1kPa.
Rate this question :
The condition of air in a closed room is described as follows. Temperature 25°C, relative humidity = 60%, pressure = 104 kPa. If all the water vapor is removed from the room without changing the temperature, what will be the new pressure? The saturation vapor pressure at 25°C = 3.2 kPa.HC Verma - Concepts of Physics Part 2
The weather report reads, “Temperature 20°C: Relative humidity 100%”. What is the dew point?HC Verma - Concepts of Physics Part 2
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.HC Verma - Concepts of Physics Part 2
Pure water vapour is trapped in a vessel of volume 10 cm3. The relative humidity is 40%. The vapour is compressed slowly and isothermally. Find the volume of the vapour at which it will start condensing.HC Verma - Concepts of Physics Part 2
The temperature and the dew point in an open room are 20°C and 10°C. If the room temperature drops to 15 °C, what will be the new dew point?HC Verma - Concepts of Physics Part 2
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg. The length of the gas column in the vessel is 20 cm. The atmospheric pressure is 100 kPa. The vessel is now taken into a spaceship revolving round the earth as a satellite. The air pressure in the spaceship is maintained at 100 kPa. Find the length of the gas column in the cylinder.HC Verma - Concepts of Physics Part 2
Figure shows a large closed cylindrical tank containing water. Initially the air trapped above the water surface has a height h0 and pressure 2p0 where p0 is the atmospheric pressure. There is a hole in the wall of the tank at a depth h1 below the top from which water comes out. A long vertical tube is connected as shown.
(a) Find the height h2 of the water in the long tube above the top initially.
(b) Find the speed with which water comes out of the hole.
(c) Find the height of the water in the long tube above the top when the water stops coming out of the hole.
HC Verma - Concepts of Physics Part 2
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg (figure). The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
HC Verma - Concepts of Physics Part 2
Find the number of molecules in 1 cm3 of an ideal gas at 0°C and at a pressure of 10–5 mm of mercury.HC Verma - Concepts of Physics Part 2
Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?HC Verma - Concepts of Physics Part 2