Refer to Exercise Assume that and are known with negligible uncertainty. Assume the mass is . Estimate , and find the relative uncertainty in the estimate.

Solution:

Step 1 of 1:

The change in temperature of an iron bar about by a transfer of heat is

Where is the amount of heat transferred.

Here .

m is the mass of the bar.

Here kg and

c is the the specific heat of iron.

Here c = 448 J/Kg0C.

Our goal is:

We need to find the estimate value of the and the relative uncertainty in the estimate.

Now we have to find the estimate value of the .

From the given information we have = 1210, m = 0.75, c = 448,

Consider,

Substitute all the values in the above equation.

=

=

= 3.6011

Therefore, = 3.6011.

Again consider .

Then,

Now we differentiate above equation with respect to “m” then

=

=

=

=

=

=

=

= -4.8015

Therefore, = -4.8015.

Now we have to find the estimate of uncertainty.

Then the estimate of uncertainty is given by

=

Here

= (4.8015)(0.01)

= 0.0480

Hence,

Therefore, The estimate of uncertainty is 0.0480.

Conclusion:

The estimate of uncertainty is 0.0480.