Goal Apply the temperature conversion formulas. Problem The temperature gradient between the skin and the air is regulated by cutaneous $($skin$)$ blood flow. If the cutaneous blood vessels are constricted, the skin temperature and the temperature of the environment will be about the same. When the vessels are dilated, more blood is brought to the surface. Suppose during dilation the skin warms from $72\mathrm{.}0\backslash$deg F to $84\mathrm{.}0\backslash$deg F$.($a$)$ Convert these temperatures to Celsius and find the difference. $($b$)$ Convert the temperatures to Kelvin, again finding the difference. Strategy This is a matter of applying the conversion formulas, as follows. TC & $=$ & T $273\mathrm{.}15$ TF & $=$ & $95$ TC $+32$ TC & $=$ & $59($TF $32)$ For part $($b$),$ it's easiest to use the answers for Celsius rather than develop another set of conversion equations. Solution $($a$)$ Convert the temperatures from Fahrenheit to Celsius and find the difference. Convert the lower temperature. TC $=59($TF $32\mathrm{.}0)=59(72\mathrm{.}032\mathrm{.}0)=22\mathrm{.}2\backslash$deg C Convert the upper temperature. TC $=59($TF $32\mathrm{.}0)=59(84\mathrm{.}032\mathrm{.}0)=28\mathrm{.}9\backslash$deg C Find the difference of the two temperatures. $\backslash$Delta TC $=28\mathrm{.}9\backslash$deg C $22\mathrm{.}2\backslash$deg C $=6\mathrm{.}7\backslash$deg C $($b$)$ Convert the temperatures from Fahrenheit to Kelvin and find their difference. Convert the lower temperature, using the answers for Celsius found in part $($a$).$ TC $=$ T $273\mathrm{.}15->$ T $=$ TC $+273\mathrm{.}15$ T $=22\mathrm{.}2+273\mathrm{.}15=295\mathrm{.}4$ K Convert the upper temperature. T $=28\mathrm{.}9+273\mathrm{.}15=302\mathrm{.}1$ K Find the difference of the two temperatures. $\backslash$Delta T $=302\mathrm{.}1$ K $295\mathrm{.}4$ K $=6\mathrm{.}7$ K Remarks The change in temperature in Kelvin and Celsius is the same, as it should be$.$ Question Which represents a larger temperature change, a Celsius degree or a Fahrenheit degree? Fahrenheit Celsius One degree is the same on either scale. It depends on the initial temperature. It's subjective and depends on the observer's judgment. Correct: Your answer is correct. Practice It Use the worked example above to help you solve this problem. The temperature gradient between the skin and the air is regulated by cutaneous $($skin$)$ blood flow. If the cutaneous blood vessels are constricted, the skin temperature and the temperature of the environment will be about the same. When the vessels are dilated, more blood is brought to the surface. Suppose that during dilation the skin warms from $71\mathrm{.}7\backslash$deg F to $80\mathrm{.}7\backslash$deg F$.($a$)$ Convert these temperatures to Celsius and find the difference. lower temperature $\backslash$deg C upper temperature $\backslash$deg C difference $\backslash$deg C $($b$)$ Convert the temperatures to Kelvin, again finding the difference. lower temperature K upper temperature K difference K Exercise Core body temperature can rise from $98\mathrm{.}6\backslash$deg F to $105\backslash$deg F during extreme exercise, such as a marathon run. Such elevated temperatures can also be caused by viral or bacterial infections or tumors and are dangerous if sustained. $($a$)$ Convert the given temperatures to Celsius and find the difference. lower temperature $\backslash$deg C upper temperature $\backslash$deg C difference $\backslash$deg C $($b$)$ Convert the temperatures to Kelvin, again finding the difference. lower temperature K upper temperature K difference K