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In a vessel, the gas is at a pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be [NEET Kar. 2013]
- a)4P
- b)2P
- c)P
- d)P/2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a vessel, the gas is at a pressure P. If the mass of all the molecu...
When mass is halved and speed is doubled then Resultant pressure,
= 2 P.
= 2 P.Most Upvoted Answer
In a vessel, the gas is at a pressure P. If the mass of all the molecu...
Given: Gas at pressure P, mass of molecules halved, speed of molecules doubled.
Pressure is directly proportional to the number of molecules and their average kinetic energy.
When the mass of molecules is halved, the number of molecules will double.
When the speed of molecules is doubled, their average kinetic energy will increase by a factor of 4.
Therefore, the total effect on pressure will be:
Pressure ∝ (number of molecules) x (average kinetic energy per molecule)
New pressure = (2 x number of molecules) x (4 x average kinetic energy per molecule)
New pressure = 8 x (number of molecules) x (average kinetic energy per molecule)
New pressure = 8P
Therefore, the resultant pressure will be 2P.
Pressure is directly proportional to the number of molecules and their average kinetic energy.
When the mass of molecules is halved, the number of molecules will double.
When the speed of molecules is doubled, their average kinetic energy will increase by a factor of 4.
Therefore, the total effect on pressure will be:
Pressure ∝ (number of molecules) x (average kinetic energy per molecule)
New pressure = (2 x number of molecules) x (4 x average kinetic energy per molecule)
New pressure = 8 x (number of molecules) x (average kinetic energy per molecule)
New pressure = 8P
Therefore, the resultant pressure will be 2P.
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