The discussion centers on the calculation of temperature from the internal energy of argon atoms using the formula U=3/2 NKbT. A participant successfully rearranged the equation to T=(2U)/(3NKb) and calculated the temperature to be approximately 281.4 K, while the expected value was 282 K. The discrepancy was attributed to a round-off error and the suggestion to use a more precise value for the Boltzmann constant, k_B=1.38×10^(-23) J/K. The atomic mass of argon was confirmed as 39.95 u, which aligns with the calculated results.
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I rearranged u=3/2NkbT, to get T=(2U)/(3NKb). Then i changed from mass to molecules, by taking N=(m/M)x(avogardos)=(6.46/39.9)x6.02x10^23=9.75x10^22. I plotted in the values; T=(2x568)/(9.75x10^22 x 1.3x10^-23 x3) =298K. The value given in the solution is 282K.kuruman said:Please show us what answer you got and how you got it. Without this information we are as much in the dark as you are.
Thank you!kuruman said:I got 281.4 K. I think you have a round-off error. Use the more accurate value ##k_B=1.38\times10^{23}~\mathrm{J/K}## for the Boltzmann constant.
BTW, Welcome to PF!
With an atomic mass of 39.95 u for Argon I got 281.8 K which rounds off to your given answer.