How Do You Calculate the R Value of an Unknown Specimen Using a Hot Box?

[Jway]

Homework Statement

Determine the R value of the unknown specimen using a conventional hot box.

Surface area of the specimen is 0.009 m2.
Initial Hot Room Temperature = T Hot Initial = 30 ° C = 303.15 K
Initial Cold Room Temperature = T Cold Initial = 20 °C = 293.15 K

Time for both rooms reach to equilibrium = 2 hours = 7200 seconds
Temperature after 2 hours in hot room = T Hot final = 22 °C = 295.15 K
Temperature after 2 hours in cold room = T Cold Final = 22 °C = 295.15 K
The gas in Hot room is Specific heat capacities = 1 J/(kg K) and masses = 1 kg
The gas in Cold room is Specific heat capacity = 1 J/(kg K) and masses = 1 kg

Homework Equations

R Value = dT x A / Q
Q = m x c dt / time

3. The Attempt at a Solution

Determine rate of heat flow.

Q = m x c x (T Cold Final - T Cold Initial ) / Time difference

= 1 kg x 1 J/(kg K) x (295.15 K – 293.15 K) / 7200 sec

= 2.78e-4 J per SecDetermine R value

R Value = dT x A / Q

= ((T Hot Initial - T Cold Final) x A) / Q

= ((303.15 K – 293.15 K) x 0.009 m2 ) / 2.78e-4 J per Sec

= 324

 

[KataKoniK]

J/(m2 K per sec)

Based on the given information, the R value of the unknown specimen is 324 J/(m2 K per sec). This value represents the thermal resistance of the specimen, which is a measure of how well it can resist heat flow. A higher R value indicates better insulation properties, while a lower R value indicates poor insulation. Further testing and analysis may be needed to determine the specific material and properties of the unknown specimen.