Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let the partial pressure of the gas in chamber A and B be P'A and P'B , respectively.
Applying equation of state for gas A, we get
`{P_A V}/{T_A} = (P'_A2V)/T`
`rArr P'_A=(P_AT)/(2T_A)`
Similarly, For gas B :
`P'_B = (P_BT)/(2T_B)`
Total Pressure is the sum of the partial pressures . It is given by
P = P'A + P'B
= `(P_AT)/(2T_A) + (P_BT)/(2T_B)`
⇒ P = `T/2(P_A/T_A + P_B/T_B)`
⇒ `P/T` = `1/2 (P_A/T_A + P_B/T_B)`
APPEARS IN
संबंधित प्रश्न
Do you expect the gas in a cooking gas cylinder to obey the ideal gas equation?
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?
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 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
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.
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.
When a gas is heated, its temperature increases. Explain this phenomenon on the basis of the kinetic theory of gases.
Find the kinetic energy of 5 litres of a gas at STP, given the standard pressure is 1.013 × 105 N/m2.
Compare the rates of emission of heat by a blackbody maintained at 727°C and at 227°C, if the black bodies are surrounded by an enclosure (black) at 27°C. What would be the ratio of their rates of loss of heat?
Under which condition laws of Boyle, Charles, and Gay-Lussac are valid?
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.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure 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 ______.
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?
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.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
If a = 0. 72 and t = 0.04, then the value of r is ______.
Which of the following materials is diathermanous?
2000 calories of radiant heat is incident on a body. If the body absorbs 550 calories of heat, find the coefficient of emmission of the body.
