According to Newton's law of cooling, the time needed for an object at an initial temperature to cool to a temperature in an environment with ambient temperature is given by
where is a constant. Assume that for a certain type of container, . Let be the number of minutes needed to cool the container to a temperature of . Assume that and . Estimate , and find the uncertainty in the estimate.
Step 1 of 2
In this question we are asked to find the estimate of Newton’s law cooling equation and the uncertainty in the estimate.
Newton’s law cooling equation = -…………..(1)
t is the number of minutes needed to cool the container
is a initial temperature
is an ambient temperature
is a constant
is a cooling temperature
= 0.025 , = 70.1 ± 0.2°F, = 35.7 ± 0.1 °F and
The quantity which we are estimating has several measurements. In this question we are measuring the initial temperature and ambient temperature . These quantity mentioned here is uncertain and independent measurements.
So here we can use the following basic formula.
Where , ,........, are independent measurements and uncertainties are , ,.........,
Equation 2 is called the multivariate propagation of error formula.