Advertisements
Advertisements
प्रश्न
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.
उत्तर
Here ,
Initial pressure = Atmospheric pressure + pressure due to mercury
⇒ P1 = P0 + PHg
Let the CSA of the tube be A.
P1 = 0.76 + 0.2 = 0.96 m Hg
T1 = T2 = T
V1 = 0.43 A
If the tube is slanted , then the atmospheric pressure P0 remains the same . only the PHg changes
`P_2 = P_0 + P_Hg cos60^circ` = 0.76 + 0.2 × 0.5 = 0.86
`P_1V_1 = P_2V_2`
⇒ `V_2 = (P_1V_1)/P_2 = (0.96×0.43A)/0.86`
Let the length of the air column be l.
⇒ Al = `(P_1V_1)/P_2 = (0.96×0.43A)/0.86`
⇒ l = 0.48 m
⇒ l = 48 cm
APPEARS IN
संबंधित प्रश्न
Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.
Using figure, find the boiling point of methyl alcohol at 1 atm (760 mm of mercury) and at 0.5 atm.
Answer in brief:
A gas in a cylinder is at pressure P. If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then find the resultant pressure.
Answer in brief:
Show that rms velocity of an oxygen molecule is `sqrt2` times that of a sulfur dioxide molecule at S.T.P.
If the density of oxygen is 1.44 kg/m3 at a pressure of 105 N/m2, find the root mean square velocity of oxygen molecules.
Calculate the average molecular kinetic energy
- per kmol
- per kg
- per molecule
of oxygen at 127°C, given that the molecular weight of oxygen is 32, R is 8.31 J mol−1K−1 and Avogadro’s number NA is 6.02 × 1023 molecules mol−1.
Earth’s mean temperature can be assumed to be 280 K. How will the curve of blackbody radiation look like for this temperature? Find out λmax. In which part of the electromagnetic spectrum, does this value lie? (Take Wien's constant b = 2.897 × 10−3 m K)
Find the temperature of a blackbody if its spectrum has a peak at (a) λmax = 700 nm (visible), (b) λmax = 3 cm (microwave region) (c) λmax = 3 m (short radio waves). (Take Wien’s constant b = 2.897 × 10-3 m.K).
Why the temperature of all bodies remains constant at room temperature?
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.
What is the microscopic origin of temperature?
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 becomes equal to 0.49 eV at a temperature about (Boltzmann constant = 1.38 x 10-23 JK-1) ____________.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure 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 ______.
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 ______.
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.
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.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
