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.
Advertisements
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?
A gas is kept in an enclosure. The pressure of the gas is reduced by pumping out some gas. Will the temperature of the gas decrease by Charles's low?
When you come out of a river after a dip, you feel cold. Explain.
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
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.
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
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.
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 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.
Answer in brief:
Show that rms velocity of an oxygen molecule is `sqrt2` times that of a sulfur dioxide molecule at S.T.P.
When a gas is heated, its temperature increases. Explain this phenomenon on the basis of the kinetic theory of gases.
Energy is emitted from a hole in an electric furnace at the rate of 20 W when the temperature of the furnace is 727°C. What is the area of the hole? (Take Stefan’s constant σ to be 5.7 × 10-8 Js-1 m-2K-4.)
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?
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.
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
The graph of kinetic energy against the frequency v of incident light is as shown in the figure. The slope of the graph and intercept on X-axis respectively are ______.
The average K.E. of hydrogen molecules at 27° C is E. The average K.E. at 627° C is ____________.
The average translational kinetic energy of a molecule in a gas is 'E1'. The kinetic energy of the electron (e) accelerated from rest through p.d. 'V' volt is 'E2'. The temperature at which E1 = E2 is possible, 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 ______.
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 ______.
Explain why there is no atmosphere on moon.
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 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 ______.
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 t = 0.04, then the value of r is ______.
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
