Question

3.18 calculate the unknown temperature in each of the following: a. 25 °c =____ °f b. 155 °c =__ °f c. -25 °f =__ °c d. 224 k =__ °c e. 145 °c =____ k

Explanation:

Step1: Recall Celsius - Fahrenheit conversion formula

The formula to convert Celsius ($C$) to Fahrenheit ($F$) is $F=\frac{9}{5}C + 32$. The formula to convert Fahrenheit to Celsius is $C=\frac{5}{9}(F - 32)$. The formula to convert Kelvin ($K$) to Celsius is $C=K - 273.15$ and to convert Celsius to Kelvin is $K = C+273.15$.

Step2: Solve part a

For $C = 25^{\circ}C$, using $F=\frac{9}{5}C + 32$, we have $F=\frac{9}{5}\times25+32$. First, $\frac{9}{5}\times25=45$, then $45 + 32=77$. So $25^{\circ}C = 77^{\circ}F$.

Step3: Solve part b

For $C = 155^{\circ}C$, using $F=\frac{9}{5}C + 32$, we have $F=\frac{9}{5}\times155+32$. $\frac{9}{5}\times155 = 9\times31=279$, then $279+32 = 311$. So $155^{\circ}C=311^{\circ}F$.

Step4: Solve part c

For $F=-25^{\circ}F$, using $C=\frac{5}{9}(F - 32)$, we have $C=\frac{5}{9}(-25 - 32)=\frac{5}{9}\times(-57)=-\frac{285}{9}\approx - 31.7^{\circ}C$.

Step5: Solve part d

For $K = 224K$, using $C=K - 273.15$, we have $C=224 - 273.15=-49.15^{\circ}C$.

Step6: Solve part e

For $C = 145^{\circ}C$, using $K = C + 273.15$, we have $K=145+273.15 = 418.15K$.

Answer:

a. $77^{\circ}F$
b. $311^{\circ}F$
c. $-31.7^{\circ}C$
d. $-49.15^{\circ}C$
e. $418.15K$