A bathtub is filled to a depth of $30$ cm with water whose temperature is $55\backslash$deg C$.$ The side walls, front, and

back of the tub have a surface temperature of $22\backslash$deg C and they receive heat from the water. The tub sides

can be approximated as vertical walls being $120$ cm long. The front and back are $76$ cm wide. Estimate

the heat convected to the tub walls.

$5.$ A satellite in orbit uses solar cells to convert sunlight to power. A preliminary analysis determines that the

plate will radiate $14000$ W of heat into space when not facing the sun. If the plate is $180$ x $180$ cm$2,$

determine the surface temperature of the plate. Assume $\backslash$epsi $=0\mathrm{.}85$

$6.$ The deep human body temperature of a healthy person remains constant at $37\backslash$deg C while the temperature

and the humidity of the environment change with time. Discuss the heat transfer mechanisms between the

human body and the environment both in summer and winter and explain how a person can keep cooler

in summer and warmer in winter.