Madeline Horn edited subsection_Analysis_Error_analysis_The__.tex  over 8 years ago

Commit id: 1a8b245275eec0adc200c4e109181ff48b62e385

deletions | additions      

       

Error analysis  The discrepancy between our result ($1.46 \pm0.0054 \cdot 10^{-23}\textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$ and $1.46 \pm0.0052  \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$) and the accepted Boltzmann constant ($1.38 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$)is approximately 5.8\% . Both sets of data we obtained (with a $1\textrm{k}\Omega$ resister and a $10\textrm{k}\Omega$) gave a consistent value for the Boltzmann constant which is a matter of accuracy rather than precision, so this error is most likely a systematic error. Assuming that our thermometer is accurate (for room temperature), the temperature within the instrument, where the resister is, may be higher. As we can see in Eq.~ \ref{eq:boltzmann}, with a higher $\textrm{T(K)}$, we would have a lower $\textrm{K}_\textrm{B}$ value which is opposite to what our value is, so this is unlikely what is causing the error.