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P Keeping the Number of Moles, Volume and Temperature the Same, Which of the Following Are the Same for All Ideal Gases?

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प्रश्न

Keeping the number of moles, volume and temperature the same, which of the following are the same for all ideal gases?

विकल्प

  • Rms speed of a molecule

  • Density

  • Pressure

  • Average magnitude of momentum.

MCQ
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उत्तर

Pressure

Pressure of an ideal gas is given by PV = \[\frac{1}{3}mn u^2\] .

We know that pressure depends on volume, number of molecules and root mean square velocity. Also, root mean square velocity depends on the temperature of the gas. Since the number of molecules, volume and temperature are constant, pressure of the gas will not change. 
shaalaa.com
Interpretation of Temperature in Kinetic Theory - Introduction of Kinetic Theory of an Ideal Gas
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 24: Kinetic Theory of Gases - MCQ [पृष्ठ ३४]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 24 Kinetic Theory of Gases
MCQ | Q 4 | पृष्ठ ३४

संबंधित प्रश्न

Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium?


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


A sample of 0.177 g of an ideal gas occupies 1000 cm3 at STP. Calculate the rms speed of the gas molecules.


A vessel containing one mole of a monatomic ideal gas (molecular weight = 20 g mol−1) is moving on a floor at a speed of 50 m s−1. The vessel is stopped suddenly. Assuming that the mechanical energy lost has gone into the internal energy of the gas, find the rise in its temperature.


The figure shows a cylindrical container containing oxygen (γ = 1.4) and closed by a 50-kg frictionless piston. The area of cross-section is 100 cm2, atmospheric pressure is 100 kPa and g is 10 m s−2. The cylinder is slowly heated for some time. Find the amount of heat supplied to the gas if the piston moves out through a distance of 20 cm.


An amount Q of heat is added to a monatomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding. Find the molar heat capacity for the process


An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation p = kV. Show that the molar heat capacity of the gas for the process is given by `"C" ="C"_"v" +"R"/2.`


Half mole of an ideal gas (γ = 5/3) is taken through the cycle abcda, as shown in the figure. Take  `"R" = 25/3"J""K"^-1 "mol"^-1 `. (a) Find the temperature of the gas in the states a, b, c and d. (b) Find the amount of heat supplied in the processes ab and bc. (c) Find the amount of heat liberated in the processes cd and da.


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.


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.


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.


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 ______.


Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory `pV = 2/3` E, E is ______.

  1. the total energy per unit volume.
  2. only the translational part of energy because rotational energy is very small compared to the translational energy.
  3. only the translational part of the energy because during collisions with the wall pressure relates to change in linear momentum.
  4. the translational part of the energy because rotational energies of molecules can be of either sign and its average over all the molecules is zero.

In a diatomic molecule, the rotational energy at a given temperature ______.

  1. obeys Maxwell’s distribution.
  2. have the same value for all molecules.
  3. equals the translational kinetic energy for each molecule.
  4. is (2/3)rd the translational kinetic energy for each molecule.

The container shown in figure has two chambers, separated by a partition, of volumes V1 = 2.0 litre and V2 = 3.0 litre. The chambers contain µ1 = 4.0 and µ2 = 5.0 moles of a gas at pressures p1 = 1.00 atm and p2 = 2.00 atm. Calculate the pressure after the partition is removed and the mixture attains equilibrium.

V1 V2
µ1, p1 µ2
  p2

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