Question

Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool 1.15 °C. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering 31.4 °C. What is the difference between the higher and lower temperatures in (a) Fahrenheit degrees and (b) kelvins?

Answer 1

Answer:54.45$^{0}F$,30.25$K$

Explanation:

Let $t_{1f}$ be the low temperature in fahrenheit.

Let $t_{2f}$ be the high temperature in fahrenheit.

Let $t_{1k}$ be the low temperature in Kelvin.

Let $t_{2k}$ be the high temperature in Kelvin.

Question a:

As we know $\frac{c}{5}=\frac{F-32}{9}$

$\frac{1.15}{5}=\frac{t_{1f}-32}{9}$

$t_{1f}=34.07^{0}F$

$\frac{31.4}{5}=\frac{t_{2f}-32}{9}$

$t_{2f}=88.52^{0}F$

So the difference is $t_{2f}-t_{1f}=54.45^{0}F$

Question b:

As we know $c+273=k$

$1.15+273=t_{1k}$

$t_{1k}=274.15K$

$31.4+273=t_{2k}$

$t_{2k}=304.4K$

So the difference is $t_{2k}-t_{1k}=30.25K$