Question

Air temperature rises from a morning low of 42°F to an afternoon high of 70°F. (a) Express these temperatures in °R, K, and °C. (b) Determine the temperature change in °F, °R, K, and °C from morning low to afternoon high. (c) What conclusion do you draw about temperature change for °F and °R scales? (d) What conclusion do you draw about temperature change for °C and K scales?

Answer 1

Explanation:

The Fahrenheit temperature conversion formulas are:

$^\circ C=\frac{5}{9}(^\circ F-32)\\R=(^\circ F +459.670)\\K=\frac{5}{9}(^\circ F-32) +273.150$

a) Using the previous equations we obtain the values of the temperatures in all scales:

$\frac{5}{9}(42^\circ F-32)=5.555^\circ C \\(42^\circ F +459.670)=501.670R\\\frac{5}{9}(42^\circ F-32) +273.150=278.705K\\\frac{5}{9}(70^\circ F-32)=21.111^\circ C \\(70^\circ F +459.670)=529.670R\\\frac{5}{9}(70^\circ F-32) +273.15=294.261K$

b)

$\Delta T(^\circ F)=70^\circ F-42^\circ F=28^\circ F\\\Delta T(R)=529.670R-501.670R=28R\\\Delta T(^\circ C)=21.111^\circ C-5.555^\circ C=15.556^\circ C\\\Delta T(K)=294.261K-278.705K=15.556K$

c) The temperature change in these scales corresponds to the same number (28). So, a change of one degree  in Rankine scale is equal to a change of one degree  in Fahrenheit scale.

d)The temperature change in these scales corresponds to the same number (15.556), So, a change of one degree  in Celsius scale is equal to a change of one degree  in Kelvin scale.