Advertisements
Advertisements
Question
Two vessels A and B are filled with the same gas where the volume, temperature, and pressure in vessel A is twice the volume, temperature, and pressure in vessel B. Calculate the ratio of the number of molecules of the gas in vessel A to that in vessel B.
Solution
Data: VA = 2VB, TA = 2TB, PA = 2PB
PV = nRT
or PV = NkBT
Find: `"N"_"A"/"N"_"B"` = ?
∴ The number of molecules, N = `"PV"/("k"_"B""T")`
∴ NA = `("P"_"A""V"_"A")/("k"_"B""T"_"A")` and NB = `("P"_"B""V"_"B")/("k"_"B""T"_"B")`
∴ `"N"_"A"/"N"_"B" = ("P"_"A"/"P"_"B")("V"_"A"/"V"_"B")("T"_"B"/"T"_"A")`
∴ `"N"_"A"/"N"_"B" = ((2"P"_"B")/"P"_"B")((2"V"_"B")/"V"_"B")("T"_"B"/(2"T"_"B"))`
∴ `"N"_"A"/"N"_"B" = cancel(2) xx 2 xx 1/cancel(2)`
∴ `"N"_"A"/"N"_"B" = 2/1`
∴ `"N"_"A"/"N"_"B"` = 2 : 1
This is the required ratio.
APPEARS IN
RELATED QUESTIONS
It is said that the assumptions of kinetic theory are good for gases having low densities. Suppose a container is so evacuated that only one molecule is left in it. Which of the assumptions of kinetic theory will not be valid for such a situation? Can we assign a temperature to this gas?
The average translational kinetic energy of air molecules is 0.040 eV (1 eV = 1.6 × 10−19J). Calculate the temperature of the air. Boltzmann constant k = 1.38 × 10−23 J K−1.
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
An ideal gas is trapped between a mercury column and the closed-end of a narrow vertical tube of uniform base containing the column. The upper end of the tube is open to the atmosphere. The atmospheric pressure equals 76 cm of mercury. The lengths of the mercury column and the trapped air column are 20 cm and 43 cm respectively. What will be the length of the air column when the tube is tilted slowly in a vertical plane through an angle of 60°? Assume the temperature to remain constant.
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).
Answer in brief:
Compare the rms speed of hydrogen molecules at 127ºC with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
The number of degrees of freedom, for the vibrational motion of a polyatomic molecule, depends on the ______
Calculate the value of λmax for radiation from a body having a surface temperature of 3000 K. (b = 2.897 x 10-3 m K)
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)
Under which condition laws of Boyle, Charles, and Gay-Lussac are valid?
On what, the values of absorption coefficient, reflection coefficient, and transmission coefficient depend, in addition to the material of the object on which the radiation is an incident?
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
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 ____________.
Average kinetic energy of H2 molecule at 300K is 'E'. At the same temperature, average kinetic energy of O2 molecule will be ______.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure is ______.
A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (Figure). If the temperature is increased ______.
The molecules of a given mass of a gas have root mean square speeds of 100 ms−1 at 27°C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?
An insulated container containing monoatomic gas of molar mass m is moving with a velocity vo. If the container is suddenly stopped, find the change in temperature.
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.
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, KP are related as ______.
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 ______.
If a = 0. 72 and t = 0.04, then the value of r is ______.
At what temperature will therms velocity of a gas be four times its value at STP?
