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Heat and Thermodynamics question

2013 · Q161
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Heat and Thermodynamics question

2013 · Q161

NEETPhysicsHeat and ThermodynamicsMCQ+4 / −1
In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be
  1. A
    2P
  2. B
    P
  3. C
    P/2
  4. D
    4P
View written solutionFree

Correct answer: A

As P=13mNVvrms2P = {1 \over 3}{{mN} \over V}v_{rms}^2P=31​VmN​vrms2​   ...(i)

where m is the mass of each molecule, N is the total number of molecules, V is the volume of the gas. When mass of all the molecules is halved and their speed is doubled, then the pressure will be

P′=13(m2)×NV×(2vrms)2P' = {1 \over 3}\left( {{m \over 2}} \right) \times {N \over V} \times {\left( {2{v_{rms}}} \right)^2}P′=31​(2m​)×VN​×(2vrms​)2

=23mNVvrms2=2P = {2 \over 3}{{mN} \over V}v_{rms}^2 = 2P=32​VmN​vrms2​=2P   (Using (i))

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