Answer:
The net energy transfer from the student's body during the 20-min ride to school is 139.164 BTU.
Explanation:
From Heat Transfer we determine that heat transfer rate due to electromagnetic radiation (
), measured in BTU per hour, is represented by this formula:
(1)
Where:
- Emissivity, dimensionless.
- Surface area of the student, measured in square feet.
- Stefan-Boltzmann constant, measured in BTU per hour-square feet-quartic Rankine.
- Temperature of the student, measured in Rankine.
- Temperature of the bus, measured in Rankine.
If we know that
,
,
,
and
, then the heat transfer rate due to electromagnetic radiation is:
![\dot Q = (0.90)\cdot (16.188\,ft^{2})\cdot \left(1.714\times 10^{-9}\,\frac{BTU}{h\cdot ft^{2}\cdot R^{4}} \right)\cdot [(554.07\,R)^{4}-(527.67\,R)^{4}]](https://tex.z-dn.net/?f=%5Cdot%20Q%20%3D%20%280.90%29%5Ccdot%20%2816.188%5C%2Cft%5E%7B2%7D%29%5Ccdot%20%5Cleft%281.714%5Ctimes%2010%5E%7B-9%7D%5C%2C%5Cfrac%7BBTU%7D%7Bh%5Ccdot%20ft%5E%7B2%7D%5Ccdot%20R%5E%7B4%7D%7D%20%5Cright%29%5Ccdot%20%5B%28554.07%5C%2CR%29%5E%7B4%7D-%28527.67%5C%2CR%29%5E%7B4%7D%5D)
![\dot Q = 417.492\,\frac{BTU}{h}](https://tex.z-dn.net/?f=%5Cdot%20Q%20%3D%20417.492%5C%2C%5Cfrac%7BBTU%7D%7Bh%7D)
Under the consideration of steady heat transfer we find that the net energy transfer from the student's body during the 20 min-ride to school is:
(2)
Where
is the heat transfer time, measured in hours.
If we know that
and
, then the net energy transfer is:
![Q = \left(417.492\,\frac{BTU}{h} \right)\cdot \left(\frac{1}{3}\,h \right)](https://tex.z-dn.net/?f=Q%20%3D%20%5Cleft%28417.492%5C%2C%5Cfrac%7BBTU%7D%7Bh%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5C%2Ch%20%5Cright%29)
![Q = 139.164\,BTU](https://tex.z-dn.net/?f=Q%20%3D%20139.164%5C%2CBTU)
The net energy transfer from the student's body during the 20-min ride to school is 139.164 BTU.