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
Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.
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
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 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 ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg in figure. The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
The condition of air in a closed room is described as follows. Temperature = 25°C, relative humidity = 60%, pressure = 104 kPa. If all the water vapour is removed from the room without changing the temperature, what will be the new pressure? The saturation vapour pressure at 25°C − 3.2 kPa.
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.
Calculate the ratio of the mean square speeds of molecules of a gas at 30 K and 120 K.
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.)
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).
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.
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
Average kinetic energy of H2 molecule at 300K is 'E'. At the same temperature, average kinetic energy of O2 molecule will be ______.
Explain why there is no atmosphere on moon.
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, KP are related as ______.
Two gases A and B are at absolute temperatures of 360 K and 420 K, respectively. The ratio of the average kinetic energy of the molecules of gas B to that of gas A is ______.
