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 the specific heat capacity (c) of water based on your data and the accepted value, you can use the concept of propagation of uncertainty. Here's how you can do it:

1. Calculate the difference between your experimental value of c and the accepted value: Δc = |c_experimental - c_accepted| = |4438 J/(kg·°C) - 4180 J/(kg·°C)| = 258 J/(kg·°C)
2. Next, you need to determine the uncertainty in your experimental value of c. This uncertainty arises from the scatter or variability in your data and can be calculated as the standard error of the slope of your regression line.
3. If you have the data points for Q vs. ΔTemperature, you can perform linear regression analysis on that data to obtain the slope of the line (which you've already done) and the standard error of the slope.
4. The standard error of the slope, denoted as SE(β), is a measure of how uncertain your slope value is based on the scatter in the data points. This value depends on your data and the regression analysis method you used. You can use statistical software or tools like Excel to compute this standard error.
5. Once you have SE(β), you can use it to calculate the uncertainty in your experimental value of c using the following formula:
6. Δc_experimental = |Slope of Regression Line - c_accepted| ± SE(β)

So, your uncertainty in the specific heat capacity of water would be Δc_experimental = 258 J/(kg·°C) ± SE(β).

Remember to report your uncertainty as both a positive and negative value, which represents the range within which you can reasonably expect the true value of c to lie based on your experimental data and analysis.