Answer:
The specific heat of the unknown material is 131.750 joules per kilogram-degree Celsius.
Explanation:
Let suppose that sphere is cooled down at steady state, then we can estimate the rate of heat transfer (
), measured in watts, that is, joules per second, by the following formula:
(1)
Where:
- Mass of the sphere, measured in kilograms.
- Specific heat of the material, measured in joules per kilogram-degree Celsius.
,
- Initial and final temperatures of the sphere, measured in degrees Celsius.
- Time, measured in seconds.
In addition, we assume that both spheres experiment the same heat transfer rate, then we have the following identity:
(2)
Where:
,
- Masses of the iron and unknown spheres, measured in kilograms.
,
- Times of the iron and unknown spheres, measured in seconds.
,
- Specific heats of the iron and unknown materials, measured in joules per kilogram-degree Celsius.

If we know that
,
,
,
and
, then the specific heat of the unknown material is:


Then, the specific heat of the unknown material is 131.750 joules per kilogram-degree Celsius.