Four tanks A, B, C, and D are filled with monatomic ideal gases. For each tank,
ID: 2298877 • Letter: F
Question
Four tanks A, B, C, and D are filled with monatomic ideal gases. For each tank, the mass of an individual atom and the rms speed of atoms are expressed in terms of "m" and "v max" respectively. Suppose that m = 1.89 * 10^-26 and v max = 900 m/s. Find the temperature of each tank.
A B C D
Mass m m 2m 2m
rms speed v rms 2v rms v rms 2v rms
A = _____________
B = ______________
C = ______________
D = ______________
Explanation / Answer
The rms speed of a monoatomic gas is given by :
rms = sqrt ( 3 * R * T / molar mass )
now molar mass = avogadro number * mass of each atom = mass of atom * 6.023 * 10^23
mass of atom = k*m = k*1.89 * 10^-26
rms = sqrt ( 3*8.314 * T / (6.023*10^23 * k* 1.89*10^-26 ) )
so.. rms = sqrt ( 2191.07179 * T / k )
for A ...
mass of atom = m
so.. k = 1
rms = v = 900
so.. 900 = sqrt ( 2191.07179 * T / k ) = sqrt ( 2191.07179 * T / 1 )
so.. Temperature = T_A = 369.6821 K = 369.6821 - 273 = 96.6821 Celcius
for B ...
mass of atom = m
so.. k = 1
rms = 2v = 2*900
so.. 1800 = sqrt ( 2191.07179 * T / k ) = sqrt ( 2191.07179 * T / 1 )
so.. Temperature = T_B = 1478.72836 K = 1478.72836 - 273 = 1205.72836 Celcius
for C ...
mass of atom = 2m
so.. k = 2
rms = v = 900
so.. 900 = sqrt ( 2191.07179 * T / k ) = sqrt ( 2191.07179 * T / 2 )
so.. Temperature = T_C = 739.36418 K = 739.36418 - 273 = 466.36418 Celcius
for D ...
mass of atom = 2m
so.. k = 2
rms = 2v = 2*900
so.. 1800 = sqrt ( 2191.07179 * T / k ) = sqrt ( 2191.07179 * T / 2 )
so.. Temperature = T_D = 2957.4567 K = 2957.4567 - 273 = 2684.4567 Celcius
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