Advertisements
Advertisements
प्रश्न
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)`.
Advertisements
उत्तर
Here ,
`P_1 = 10^5 "Pa"`
`A = π(0.05)^2`
L = 0.2 m
`V = AL = 0.0016 \text ( m)^3`
`T_1 = 300 K`
`T_2 = 600 K `
`µ = 0.20`
Applying 5 variable equation of state , we get
`(P_1V)/T_1 = (P_2V)/T_2`
⇒ `P_1/T_1 = P_2/T_2`
⇒ `P_2 = T_2/T_1 × P_1 = 600/300 × 10^5`
⇒ `P_2 = 2 × 10^5`
Net pressure , `P = P_2 - P_1 = 2 × 10^5 - 10^5 = 10^5`
Total force acting on the stopper = `PA = 10^5×pi×(0.05)^2`
Applying law of friction , we get
`F = µN = 0.2N`
⇒ `N = F/µ = (10^5×pi×(0.05)^2)/0.2`
`(dN)/(dl) = N/(2pir) = (10^5×pi×(0.05)^2)/(0.2×2pi×(0.05))=0.125×10^5`
⇒ `(dN)/(dl) = 1.25×10^4 N/m`
APPEARS IN
संबंधित प्रश्न
Can we define the temperature of (a) vacuum, (b) a single molecule?
Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?
If the molecules were not allowed to collide among themselves, would you expect more evaporation or less evaporation?
When you come out of a river after a dip, you feel cold. Explain.
The mean square speed of the molecules of a gas at absolute temperature T is proportional to
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
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.
If a = 0.72 and r = 0.24, then the value of tr is ______.
Answer in brief:
Show that rms velocity of an oxygen molecule is `sqrt2` times that of a sulfur dioxide molecule at S.T.P.
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.
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)
What is the microscopic origin of temperature?
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 ______.
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 ______.
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.
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 ______.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
