Advertisements
Advertisements
प्रश्न
A gas is enclosed in a cylindrical can fitted with a piston. The walls of the can and the piston are adiabatic. The initial pressure, volume and temperature of the gas are 100 kPa, 400 cm3 and 300 K, respectively. The ratio of the specific heat capacities of the gas, Cp / Cv = 1.5. Find the pressure and the temperature of the gas if it is (a) suddenly compressed (b) slowly compressed to 100 cm3.
उत्तर
Initial pressure of the gas, P1 = 100 kPa
Initial volume of the gas,V1 = 400 cm3 = 400 × 10−6 m3
Initial temperature of the gas, T1 = 300 K
`gamma =("C"_"p")/("C"_"v") =1.5`
(a) The gas is suddenly compressed to volume, V2 = 100 cm3 .
So, this is an adiabatic process.
For an adiabatic process,
P1V1γ = P2V2γ
⇒ 105 × (400)1.5 = P2 (100)1.5
⇒ P2 =105 (4)1.5 = 800 kPa
Also,
T1Vγ−1 = T2V2γ−1
⇒ 300 × (400)1.5−1 = T2 (100)1.5−1
⇒ 300 × (400)0.5 = T2 (100)0.5
⇒ T2 = 600 K
(b) If the container is slowly compressed, the heat transfer is zero, even thought the walls are adiabatic.
Thus, the values remain same. Thus,
P2 = 800 kPa
T2 = 600 K
APPEARS IN
संबंधित प्रश्न
A gas is kept in a rigid cubical container. If a load of 10 kg is put on the top of the container, does the pressure increase?
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?
Explain why cooking is faster in a pressure cooker.
Figure shows graphs of pressure vs density for an ideal gas at two temperatures T1 and T2.
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
An air bubble of radius 2.0 mm is formed at the bottom of a 3.3 m deep river. Calculate the radius of the bubble as it comes to the surface. Atmospheric pressure = 1.0 × 105 Pa and density of water = 1000 kg m−3.
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
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.
Use R = 8.3 J K-1 mol-1
The initial pressure and volume of a given mass of a gas (Cp/Cv = γ) are p0 and V0. The gas can exchange heat with the surrounding. (a) It is slowly compressed to a volume V0/2 and then suddenly compressed to V0/4. Find the final pressure. (b) If the gas is suddenly compressed from the volume V0 to V0/2 and then slowly compressed to V0/4, what will be the final pressure?
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.
Three samples A, B and C of the same gas (γ = 1.5) have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabatic for B and isobaric for C. If the final pressures are equal for the three samples, find the ratio of the initial pressures.
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.
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.
The temperature and humidity of air are 27°C and 50% on a particular day. Calculate the amount of vapour that should be added to 1 cubic metre of air to saturate it. The saturation vapour pressure at 27°C = 3600 Pa.
Use R = 8.3 J K-1 mol-1
A cuboidal container having dimensions 2 m × 1.5 m × 0.5 m holds a mixture of 12 g of He, 36 g of Ar, and 20 g of Ne, If the container is maintained at 300 K, Find the pressure exerted by the mixture (given MHe = 4, MAr = 40, MNe = 20).
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 ______.
