Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given:
Area of the tube, A = 1 cm2 = 1 × 10−4 m2
Mass of the gas, M = 0.03 g = 0.03 × 10−3 kg
Initial pressure, P = 1 atm = 105 Pascal
Initial length of the mercury column, L = 40 cm = 0.4 m
Final length of the mercury column, L1 = 80 cm = 0.8 m
Final pressure, P' = 0.355 atm
The process is adiabatic. So,
P(V)γ = P'(V')γ
⇒ 1 × (A × 0.4)γ = 0.355 × (A × 0.8)γ
⇒ 1 × 1 = 0.355 × 2γ
`=> 1/0.355 = 2^gamma`
`gamma "log" 2 = "log"(1/0.355)`
⇒ γ =1.4941
Speed of sound in the gas,
`"v" = sqrt((gamma"P")/ρ) = sqrt ((gamma"P")/("m"/"v"))`
`"v" = sqrt ((1.4941 xx 10^5)/("m"/"v")) = sqrt ((1.4941 xx 10^5)/(( 0.03 xx 10 ^-3)/(10 ^-4 xx 1 xx 0.4)`
⇒ v = 446.33 ≈ 447 m/s
APPEARS IN
RELATED QUESTIONS
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?
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?
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
During an experiment, an ideal gas is found to obey an additional law pV2 = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.
Use R = 8.3 J K-1 mol-1
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 weather report reads, "Temperature 20°C : Relative humidity 100%". What is the dew point?
Using figure, find the boiling point of methyl alcohol at 1 atm (760 mm of mercury) and at 0.5 atm.
If a = 0.72 and r = 0.24, then the value of tr is ______.
In an ideal gas, the molecules possess ______.
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.
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.)
On what, the values of absorption coefficient, reflection coefficient, and transmission coefficient depend, in addition to the material of the object on which the radiation is an incident?
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.
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 ______.
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 average K.E.
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 ______.
