Advertisements
Advertisements
Question
An ideal gas of density 1.7 × 10−3 g cm−3 at a pressure of 1.5 × 105 Pa is filled in a Kundt's tube. When the gas is resonated at a frequency of 3.0 kHz, nodes are formed at a separation of 6.0 cm. Calculate the molar heat capacities Cp and Cv of the gas.
Advertisements
Solution
Given:
Density of the ideal gas, ρ = 1.7 × 10−3 g/cm3
= 1.7 k/gm3
Pressure of the gas, P = 1.5 × 105 Pa
R = 8.3 J/mol-K
Resonance frequency of the gas = 3.0 kHz
Node separation in the Kundt's tube
`"l"/2 = 6 "cm"`
So, l = 2×6 = 12 cm = 12 × 10−2 m
So, V = fl = 3 × 103 × 12 × 10−2
= 360 m/s
Speed of sound, V =` sqrt( (gamma"p")/ρ)`
Or `"V"^2 =( gamma"p")/ρ `
`therefore gamma =("v"^2ρ)/"P" = ((360)^2 xx 1.7 xx 10^-3)/(1.5 xx 10^5)`
= 1.4688
Using `"C"_"P" -"C"_"v" = "R" and "C"_"p"/"C"_"v" = gamma`
We know that
`"C"_"v" = "R"/(gamma-1) =8.3/0.4688`
= 17.7 J / mol -K
Cp = R +Cv =8.3 +17.7 = 26 J /mol -K
APPEARS IN
RELATED QUESTIONS
The energy of a given sample of an ideal gas depends only on its
Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium?
Keeping the number of moles, volume and temperature the same, which of the following are the same for all ideal gases?
Consider the quantity \[\frac{MkT}{pV}\] of an ideal gas where M is the mass of the gas. It depends on the
Calculate the volume of 1 mole of an ideal gas at STP.
Find the number of molecules in 1 cm3 of an ideal gas at 0°C and at a pressure of 10−5mm of mercury.
Use R = 8.31 J K-1 mol-1
Let Q and W denote the amount of heat given to an ideal gas and the work done by it in an isothermal process.
Let Q and W denote the amount of heat given to an ideal gas and the work done by it in an adiabatic process.
(a) Q = 0
(b) W = 0
(c) Q = W
(d) Q ≠ W
The ratio of the molar heat capacities of an ideal gas is Cp/Cv = 7/6. Calculate the change in internal energy of 1.0 mole of the gas when its temperature is raised by 50 K (a) keeping the pressure constant (b) keeping the volume constant and (c) adiaba
An ideal gas (Cp / Cv = γ) is taken through a process in which the pressure and the volume vary as p = aVb. Find the value of b for which the specific heat capacity in the process is zero.
An ideal gas (γ = 1.67) is taken through the process abc shown in the figure. The temperature at point a is 300 K. Calculate (a) the temperatures at b and c (b) the work done in the process (c) the amount of heat supplied in the path ab and in the path bcand (d) the change in the internal energy of the gas in the process.
The volume of an ideal gas (γ = 1.5) is changed adiabatically from 4.00 litres to 3.00 litres. Find the ratio of (a) the final pressure to the initial pressure and (b) the final temperature to the initial temperature.
An ideal gas at pressure 2.5 × 105 Pa and temperature 300 K occupies 100 cc. It is adiabatically compressed to half its original volume. Calculate (a) the final pressure (b) the final temperature and (c) the work done by the gas in the process. Take γ = 1.5
1 litre of an ideal gas (γ = 1.5) at 300 K is suddenly compressed to half its original volume. (a) Find the ratio of the final pressure to the initial pressure. (b) If the original pressure is 100 kPa, find the work done by the gas in the process. (c) What is the change in internal energy? (d) What is the final temperature? (e) The gas is now cooled to 300 K keeping its pressure constant. Calculate the work done during the process. (f) The gas is now expanded isothermally to achieve its original volume of 1 litre. Calculate the work done by the gas. (g) Calculate the total work done in the cycle.
The figure shows an adiabatic cylindrical tube of volume V0 divided in two parts by a frictionless adiabatic separator. Initially, the separator is kept in the middle, an ideal gas at pressure p1 and temperature T1 is injected into the left part and another ideal gas at pressure p2 and temperature T2 is injected into the right part. Cp/Cv = γ is the same for both the gases. The separator is slid slowly and is released at a position where it can stay in equilibrium. Find (a) the volumes of the two parts (b) the heat given to the gas in the left part and (c) the final common pressure of the gases.
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 ms–1 in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground ______.
1 mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at 300 K (Figure). One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time ______.
ABCDEFGH is a hollow cube made of an insulator (Figure). Face ABCD has positive charge on it. Inside the cube, we have ionized hydrogen. The usual kinetic theory expression for pressure ______.
- will be valid.
- will not be valid since the ions would experience forces other than due to collisions with the walls.
- will not be valid since collisions with walls would not be elastic.
- will not be valid because isotropy is lost.
In a diatomic molecule, the rotational energy at a given temperature ______.
- obeys Maxwell’s distribution.
- have the same value for all molecules.
- equals the translational kinetic energy for each molecule.
- is (2/3)rd the translational kinetic energy for each molecule.
