Advertisements
Advertisements
प्रश्न
The container shown in figure has two chambers, separated by a partition, of volumes V1 = 2.0 litre and V2 = 3.0 litre. The chambers contain µ1 = 4.0 and µ2 = 5.0 moles of a gas at pressures p1 = 1.00 atm and p2 = 2.00 atm. Calculate the pressure after the partition is removed and the mixture attains equilibrium.
| V1 | V2 |
| µ1, p1 | µ2 |
| p2 |
Advertisements
उत्तर
Consider the diagram,
| p1V1 | p2V2 |
| µ1 | µ2 |
Given, V1 = 2.0 L, V2 = 3.0 L
µ1 = 4.0 mol, µ2 = 5.0 mol
p1 = 1.00 atm, p2 = 2.00 atm
For chamber 1, p1, V1 = µ1RT1
For chamber 2, p2, V2 = µ2RT2
When the partition is removed the gases get mixed without any loss of energy. The mixture Now attains a common equilibrium pressure and the total volume of the system is the sum of the volume of individual chambers V1 and V2.
So, µ = µ1 + µ2, V = V1 + V2
From the kinetic theory of gases,
For `l` mole `pV = 2/3 E` ......`[(E = "Translational"),("Kinetic energy")]`
For `µ_1` moles, `p_1V_1 = 2/3 µ_1E_1`
For `µ_2` moles, `p_2V_2 = 2/3 µ_2E_2`
The total energy is `(µ_1E_1 + µ_2E_2) = 3/2 (p_1V_1 + p_2V_2)`
From the above relation, `pV = 2/3 E_"total" = 2/3 µE_"per mole"`
`p(V_1 + V_2) = 2/3 xx 3/2 (p_1V_1 + p_2V_2)`
`p = (p_1V_1 + p_2V_2)/(V_1 + V_2)`
= `((1.00 + 2.0 + 2.00 xx 3.0)/(2.0 + 3.0))` atm
= `8.0/5.0`
= 1.60 atm
APPEARS IN
संबंधित प्रश्न
The energy of a given sample of an ideal gas depends only on its
Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium?
The average momentum of a molecule in a sample of an ideal gas depends on
Calculate the volume of 1 mole of an ideal gas at STP.
Let Q and W denote the amount of heat given to an ideal gas and the work done by it in an isothermal process.
A rigid container of negligible heat capacity contains one mole of an ideal gas. The temperature of the gas increases by 1° C if 3.0 cal of heat is added to it. The gas may be
(a) helium
(b) argon
(c) oxygen
(d) carbon dioxide
A vessel containing one mole of a monatomic ideal gas (molecular weight = 20 g mol−1) is moving on a floor at a speed of 50 m s−1. The vessel is stopped suddenly. Assuming that the mechanical energy lost has gone into the internal energy of the gas, find the rise in its temperature.
An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation p = kV. Show that the molar heat capacity of the gas for the process is given by `"C" ="C"_"v" +"R"/2.`
Two ideal gases have the same value of Cp / Cv = γ. What will be the value of this ratio for a mixture of the two gases in the ratio 1 : 2?
An ideal gas (γ = 1.67) is taken through the process abc shown in the figure. The temperature at point a is 300 K. Calculate (a) the temperatures at b and c (b) the work done in the process (c) the amount of heat supplied in the path ab and in the path bcand (d) the change in the internal energy of the gas in the process.
An ideal gas at pressure 2.5 × 105 Pa and temperature 300 K occupies 100 cc. It is adiabatically compressed to half its original volume. Calculate (a) the final pressure (b) the final temperature and (c) the work done by the gas in the process. Take γ = 1.5
Consider a given sample of an ideal gas (Cp/Cv = γ) having initial pressure p0 and volume V0. (a) The gas is isothermally taken to a pressure p0/2 and from there, adiabatically to a pressure p0/4. Find the final volume. (b) The gas is brought back to its initial state. It is adiabatically taken to a pressure p0/2 and from there, isothermally to a pressure p0/4. Find the final volume.
Two samples A and B, of the same gas have equal volumes and pressures. The gas in sample A is expanded isothermally to double its volume and the gas in B is expanded adiabatically to double its volume. If the work done by the gas is the same for the two cases, show that γ satisfies the equation 1 − 21−γ = (γ − 1) ln2.
An ideal gas of density 1.7 × 10−3 g cm−3 at a pressure of 1.5 × 105 Pa is filled in a Kundt's tube. When the gas is resonated at a frequency of 3.0 kHz, nodes are formed at a separation of 6.0 cm. Calculate the molar heat capacities Cp and Cv of the gas.
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 ms–1 in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground ______.
We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state?
(Hydrogen molecules can be consider as spheres of radius 1 Å).
