Advertisements
Advertisements
प्रश्न
Explain, on the basis of the kinetic theory of gases, how the pressure of a gas changes if its volume is reduced at a constant temperature.
Advertisements
उत्तर १
- At constant temperature, a gas's average kinetic energy per molecule remains constant.
- When a gas's volume is lowered at a constant temperature, the number of gas molecules colliding with the container's walls per unit time increases.
- The momentum transferred per unit time per unit area, i.e. the force exerted by the gas on the walls, increases as a result.
- As a result, the gas pressure rises.
उत्तर २
Let P - be the pressure exerted by the gas
V - be the volume of the gas
N - be the number of molecule of gas
m - be the mass of each molecule of gas.
∴ Total mass of the gas, M = Nm.
From kinetic theory of gases,
`P = (1/3) (Nm)/V barv^2`
∴ Pressure exerted by gas in an enclosed vessel is
`P = 2/3 N/V (1/2mbarv^2)`
But `1/2mbarv^2` = (Kinetic energy at constant temperature)
N is number which is also constant.
∴ `P = "Constant"/V`
∴ `P ∝ 1/V`
As a result, at constant temperature, increasing the pressure of the gas reduces its volume.
APPEARS IN
संबंधित प्रश्न
When you come out of a river after a dip, you feel cold. Explain.
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
The mean speed of the molecules of a hydrogen sample equals the mean speed of the molecules of a helium sample. Calculate the ratio of the temperature of the hydrogen sample to the temperature of the helium sample.
Use R = 8.314 JK-1 mol-1
Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.
Use R = 8.3 J K-1 mol-1
Figure shows a cylindrical tube of radius 5 cm and length 20 cm. It is closed by a tight-fitting cork. The friction coefficient between the cork and the tube is 0.20. The tube contains an ideal gas at a pressure of 1 atm and a temperature of 300 K. The tube is slowly heated and it is found that the cork pops out when the temperature reaches 600 K. Let dN denote the magnitude of the normal contact force exerted by a small length dlof the cork along the periphery (see the figure). Assuming that the temperature of the gas is uniform at any instant, calculate `(dN)/(dt)`.
Figure shows a cylindrical tube of cross-sectional area A fitted with two frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the temperature of the gas is T0 and its pressure is p0 which equals the atmospheric pressure. (a) What is the tension in the wire? (b) What will be the tension if the temperature is increased to 2T0 ?
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 in 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.
The weather report reads, "Temperature 20°C : Relative humidity 100%". What is the dew point?
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 vapour is removed from the room without changing the temperature, what will be the new pressure? The saturation vapour pressure at 25°C − 3.2 kPa.
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?
An adiabatic cylindrical tube of cross-sectional area 1 cm2 is closed at one end and fitted with a piston at the other end. The tube contains 0.03 g of an ideal gas. At 1 atm pressure and at the temperature of the surrounding, the length of the gas column is 40 cm. The piston is suddenly pulled out to double the length of the column. The pressure of the gas falls to 0.355 atm. Find the speed of sound in the gas at atmospheric temperature.
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively).
Find the kinetic energy of 5 litres of a gas at STP, given the standard pressure is 1.013 × 105 N/m2.
The emissive power of a sphere of area 0.02 m2 is 0.5 kcal s-1m-2. What is the amount of heat radiated by the spherical surface in 20 seconds?
The power radiated by a perfect blackbody depends only on its ______
Above what temperature, all bodies radiate electromagnetic radiation?
If the density of nitrogen is 1.25 kg/m3 at a pressure of 105 Pa, find the root mean square velocity of nitrogen molecules.
Compare the rate of radiation of metal bodies at 727 °C and 227 °C.
When photons of energy hv fall on a metal plate of work function 'W0', photoelectrons of maximum kinetic energy 'K' are ejected. If the frequency of the radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be ______.
The average K.E. of hydrogen molecules at 27° C is E. The average K.E. at 627° C is ____________.
A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity `omega`. Its kinetic energy is ______.
The average translational kinetic energy of a molecule in a gas becomes equal to 0.49 eV at a temperature about (Boltzmann constant = 1.38 x 10-23 JK-1) ____________.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure is ______.
Two molecules of a gas have speeds of 9 × 10 6 ms−1 and 1 × 106 ms−1, respectively. What is the root mean square speed of these molecules?
Consider a rectangular block of wood moving with a velocity v0 in a gas at temperature T and mass density ρ. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to v0 is A. Show that the drag force on the block is `4ρAv_0 sqrt((KT)/m)`, where m is the mass of the gas molecule.
23Ne decays to 23Na by negative beta emission. Mass of 23Ne is 22.994465 amu mass of 23Na is 22.989768 amu. The maximum kinetic energy of emitted electrons neglecting the kinetic energy of recoiling product nucleus is ______ MeV.
When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, then the frequency of the kinetic energy is ______.
Assuming the expression for the pressure P exerted by an ideal gas, prove that the kinetic energy per unit volume of the gas is `3/2` P.
If a = 0. 72 and r = 0.24, then the value of t is ______.
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
