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Hi, I have a thermodynamics problem which I tried to solve but have no idea whether my attempt has been succesful. Here is the problem:
Initially the translational root mean squared speed of an atom of a monatomic
ideal gas is 250 m/s. The pressure and volume of the gas are each doubled while
the number of moles of the gas is kept constant. What is the final translational rms
speed of the atoms.
I used the equation: v(rms) = sqrt[(3RT)/M].
Therefore:
250 = sqrt[(3RT)/M]
I then squared both sides and took over the M (molar mass):
(3RT) = 62500M
and then divided both sides by 3:
RT = 20833(1/3)M
I then argued that becuase PV=nRT
RT = PV/n
= PVM/m (from n = m/M)
I then had the expression:
PVM/m = 20833(1/3)M
and eliminated M on both sides.
PV/m = 20833(1/3)
Therefore, by doubling the Pressure, P and Volume V:
2PV/m = 41666(2/3).
From here I just worked backwards.
2(PV/m) = 41666(2/3)
= 2(RT/M) = 41666(2/3)
and eventually got back to:
sqrt[(3RT)/M] = 250
I obviously worked in a circle...
So if anybody could give me a hint where I can get out of this circle...
That would be greatly appreciated.
Thanks
Initially the translational root mean squared speed of an atom of a monatomic
ideal gas is 250 m/s. The pressure and volume of the gas are each doubled while
the number of moles of the gas is kept constant. What is the final translational rms
speed of the atoms.
I used the equation: v(rms) = sqrt[(3RT)/M].
Therefore:
250 = sqrt[(3RT)/M]
I then squared both sides and took over the M (molar mass):
(3RT) = 62500M
and then divided both sides by 3:
RT = 20833(1/3)M
I then argued that becuase PV=nRT
RT = PV/n
= PVM/m (from n = m/M)
I then had the expression:
PVM/m = 20833(1/3)M
and eliminated M on both sides.
PV/m = 20833(1/3)
Therefore, by doubling the Pressure, P and Volume V:
2PV/m = 41666(2/3).
From here I just worked backwards.
2(PV/m) = 41666(2/3)
= 2(RT/M) = 41666(2/3)
and eventually got back to:
sqrt[(3RT)/M] = 250
I obviously worked in a circle...
So if anybody could give me a hint where I can get out of this circle...
That would be greatly appreciated.
Thanks