Advertisements
Advertisements
Question
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
Solution 1
- 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.
Solution 2
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
RELATED QUESTIONS
When we place a gas cylinder on a van and the van moves, does the kinetic energy of the molecules increase? Does the temperature increase?
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?
Is it possible to boil water at room temperature, say 30°C? If we touch a flask containing water boiling at this temperature, will it be hot?
The mean square speed of the molecules of a gas at absolute temperature T is proportional to
Which of the following quantities is the same for all ideal gases at the same temperature?
(a) The kinetic energy of 1 mole
(b) The kinetic energy of 1 g
(c) The number of molecules in 1 mole
(d) The number of molecules in 1 g
At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?
Use R = 8.314 JK-1 mol-1
Figure shows two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are pA, TA, V in the vessel A and pB, TB, V in the vessel B. The vessels are now connected through a small tube. Show that the pressure p and the temperature T satisfy `Ρ/T = 1/2 ({P_A}/{T_A}+{P_B}/{T_B))` when equilibrium is achieved.
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?
A glass contains some water at room temperature 20°C. Refrigerated water is added to it slowly. when the temperature of the glass reaches 10°C, small droplets condense on the outer surface. Calculate the relative humidity in the room. The boiling point of water at a pressure of 17.5 mm of mercury is 20°C and at 8.9 mm of mercury it is 10°C.
If a = 0.72 and r = 0.24, then the value of tr is ______.
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).
When a gas is heated, its temperature increases. Explain this phenomenon on the basis of the kinetic theory of gases.
The number of degrees of freedom, for the vibrational motion of a polyatomic molecule, depends on the ______
The power radiated by a perfect blackbody depends only on its ______
Calculate the energy radiated in one minute by a blackbody of surface area 200 cm2 at 127 °C (σ = 5.7 x 10-8 J m-2 s-1 K-4)
Above what temperature, all bodies radiate electromagnetic radiation?
What is the microscopic origin of temperature?
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 ______.
Average kinetic energy of H2 molecule at 300K is 'E'. At the same temperature, average kinetic energy of O2 molecule will be ______.
A molecule consists of two atoms each of mass 'm' and separated by a distance 'd'. At room temperature the average rotational kinetic energy is 'E', then its angular frequency is ______.
An ideal gas in a container of volume 500 cc is at a pressure of 2 × 105 N/m2. The average kinetic energy of each molecule is 6 × 10−21 J. The number of gas molecules in the container is ______.
Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P1 and P2?
An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be ______.
A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC. Rank the three types of molecules in decreasing order of rms speeds.
When the temperature of an ideal gas is increased from 27°C to 227°C, its speed is changed from 400 ms-1 to vs, and Then vs is ______.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
