Physics lab: how do i find the uncertanity of c (specific heat of water)

Question

Physics lab: how do i find the uncertanity of c (specific heat of water) , when this is the data i have: I have the mass of water= 0.2304 kg, I have the temp for every 15 second time interval, i have the Q (heat energy) for for every 15 second time interval, I ploted a regression line Q vs Delta TEmperture data and got a slope and with the slope i solved for c (specific heat of water) and got 4438 J/(kg* degrees C), The accepted value for c is 4180 J/kg oC. how do i calculate the uncertanity of specific heat?

Answer 1

To calculate the uncertainty in lab measurements, you can use the formula for the standard deviation of samples.

Sigma=square root(summation(C-C_mean)^2/(N-1)) which C is the instantaneous C measured at each data point. C_mean is the value from your regression and N is the number of data points.

For each temperature measurement every 15 seconds, you can calculate the instantaneous specific heat (C) value and the value you found for C via regression can be used as the mean value of the population. You have N number of these data points in your recordings and can find the uncertainty by plugging values in the provided formula.