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3. If the pressure of a gas is doubled while its volume is held constant, by what factor does `v_(rms)` change?
3. If the pressure of a gas is doubled while its volume is held constant, by what factor does v_(rms) change? `PV = NkT`
`v_(rms) = sqrt((3kT)/m)`
`v_2/v_1 = sqrt(2) = 1.41`
Given:
`P_2 = 2P_1`
`V` and `N` not change
Equation:
`PV = NkT`
`v_(rms) = sqrt((3kT)/m)`
Solution:
`P_1V = NkT_1` and `P_2V = NkT_2`
`=>`
`(NkT_2)/(NkT_1) = (P_2V)/(P_1V)`
`T_2/T_1 = P_2/P_1 = (2P_1)/P_1`
`T_2 = 2T_1`
`v_2/v_1 = (sqrt((3kT_2)/m))/(sqrt((3kT_1)/m))`
`v_2/v_1 = sqrt(T_2/T_1) = sqrt((2T_1)/T_1) `
`v_2/v_1 = sqrt(2) = 1.41` |