first calculate the partial derivatives of the two fromulas for each measured variable. Then you calculate the sum of the products of the errors (Dr, DR, and dh) with the squared corresponding partial derivative.and or the deviation
Example for the length of the mantle:
dm/dR = (R-r)/root(w)
dm/dr = -(R-r)/root(w)
dm/dh = h/root(w)
where w = (R-r)²+h². The squared derivatives are
(dm/dR)² = (R-r)²/w
When it comes to statistics and probability theory, standard deviation is used. It demonstrates the accuracy of your data and is used to measure both variability and diversity.
Standard deviation is calculated by taking the square root of the variance. In contrast to a high standard deviation, which indicates that the entered data points are most likely farther from the mean, a low standard deviation indicates that the entered data points are most likely closer to the mean
Approximately of steam at (assuming that the boiling point of water in this experiment is .)
Explanation:
Latent heat of condensation/evaporation of water: .
Both mass values in this question are given in grams. Hence, convert the specific heat values from this question to .
Specific heat of water: .
Specific heat of copper: .
The temperature of this calorimeter and the of water that it initially contains increased from to . Calculate the amount of energy that would be absorbed:
.
.
Hence, it would take an extra of energy to increase the temperature of the calorimeter and the of water that it initially contains from to .
Assume that it would take grams of steam at ensure that the equilibrium temperature of the system is .
In other words, of steam at would need to release as it condenses (releases latent heat) and cools down to .
Latent heat of condensation from of steam: .
Energy released when that of water from the steam cools down from to :
.
These two parts of energy should add up to . That would be exactly what it would take to raise the temperature of the calorimeter and the water that it initially contains from to .
.
Solve for :
.
Hence, it would take approximately of steam at for the equilibrium temperature of the system to be .