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Question
Answer in brief:
A gas in a cylinder is at pressure P. If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then find the resultant pressure.
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Solution
m2 = m1/3, vrms2 = 2vrms1 as the speeds of all molecules are doubled
Pressure, P = `1/3."mN"/"V"."v"^2`rms
∴ `"P"_1 = 1/3,("m"_1"N")/"V"."v"_"rms 1"^2` and
∴ `"P"_2 = 1/3,("m"_2"N")/"V"."v"_"rms 2"^2`
∴ `"P"_2/"P"_1 = ("m"_2/"m"_1)(("v"_"rms2"^2)/("v"_"rms 1"^2))`
`=("m"_2/"m"_1)(("v"_"rms 2")/("v"_"rms 1"))^2`
`= (("m"_1//3)/"m"_1)(2)^2 = 4/3`
∴ `"P"_2 = 4/3"P"_1 = 4/3"P"`
This is the resultant pressure.
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