The change in temperature of an iron bar brought about by a transfer of heat is given by , where is the amount of heat transferred, is the mass of the bar, and is the specific heat of iron. Assume that and are known with negligible uncertainty. Assume the mass is Estimate , and find the uncertainty in the estimate.

Solution 6E

Step1 of 2:

Let us consider be the change in temperature of an iron bar brought about by a transfer of heat.

Where,

= the amount of heat transferred.

= 1210 J.

m = mass of the bar.

= 0.540.01 Kg.

c = the specific heat of iron.

= 448 J/Kg0C.

We need to find the uncertainty in the estimate.

Step2 of 2:

From the given information we have = 1210, m = 0.54, c = 448,

Consider,

= 1210/(0.54)(448)

= 1210/241.92

= 5.0016

Hence, = 5.0016.

Again consider,

Differentiate above equation with respect to “m” then

=

=

=

=

=

=

=

= -9.2623

Hence, = -9.2623.

The estimate of uncertainty is given by

=

= (9.2623)(0.01)

= 0.0926

Hence,

Therefore, The estimate of uncertainty is 0.0926.

Conclusion:

The estimate of uncertainty is 0.0926.