Question

Calculate the unknown temperature in each of the following:

a.${37.0}^{\circ }\mathrm{C}=\_\_\_\_\_\_\_°F$

b.$67.3^{\circ }F=\_\_\_\_\_\_\_°C$

c. localid="1651679546288" $-{27}^{\circ }\mathrm{C}=\_\_\_\_\_\_\_°K$

d.${62}^{\circ }\mathrm{C}=\_\_\_\_\_\_\_°K$

e.${114}^{\circ }F=\_\_\_\_\_\_\_°C$

Short answer

a.${37.0}^{\circ }\mathrm{C}=98.6°F$

b.$67.3^{\circ }F=18.5°C$

c.role="math" localid="1651681461790" $-{27}^{\circ }\mathrm{C}=246K$

d.role="math" localid="1651681457064" ${62}^{\circ }\mathrm{C}=335K$

e.${114}^{\circ }F=46°C$

Step-by-step solution

Given Information (a)

(a) The unknown temperature of $37.0°C$

Explanation (a)

The smaller units by which the temperature difference with the freezing $(0°C)$and also the boiling points of water $(100°C)$are divided are called degrees.

Let us determine the conversion of $\left({37.0}^{\circ }\mathrm{C}\right)$to${}^{\circ }F$ .

Thefactor is as follows:
$T_{\mathrm{F}}=1.8\left(T_{\mathrm{C}}\right)+32$

$T_{\mathrm{F}}=66.6+32$

$T_{\mathrm{F}}={98.6}^{\circ }\mathrm{F}$

Therefore, we have

${37.0}^{\circ }\mathrm{C}={98.6}^{\circ }\mathrm{F}$

Given Information (b)

(b) The unknown temperature of$67.3°F$

Explanation (b)

(b) we've got to see the conversion of $(65.3°F)$into $°C$. Thefactor is as follows:
$T_F=1.8\left(T_{\mathrm{c}}\right)+32$
Substitute the Fahrenheit temperaturewithin the equation.

$65.3=1.8\left(T_{\mathrm{c}}\right)+32$

$1.8\left(T_{\mathrm{c}}\right)=65.3-32$

$T_{\mathrm{c}}=33.3$

$T_{\mathrm{c}}=\frac{33.3}{1.8}$

$T_{\mathrm{c}}=18.5°C$

Therefore, we have

$65.3°F=18.5°C$

Given information (c)

(c) The unknown temperature of$-27°F$

Explanation (c)

(c) Determine the conversion of $-27°F$into $K$. The factor is as follows:

$T_k=T_{\mathrm{c}}+273$

Substitute the Celsius temperature within the equation.

$T_k=-27+273$

$T_k=246K$

Therefore, we have

$-27°F=246K$

Given information (d)

The unknown temperature of$62°C$

Explanation (d)

(d) Determine the conversion of $62°C$into $K$. The factor is as follows:

$T_k=T_{\mathrm{c}}+273$

Substitute the Celsius temperature within the equation.

$T_k=62+273$

$T_k=335K$

Therefore, we have
$62°C=335K$

Given Information (e)

The unknown temperature of$114°F$

Explanation (e)

(e) Finally, we've to see the conversion of $114°F$into $°C$. The factor is as follows:

$T_{\mathrm{F}}=1.8\left(T_{\mathrm{C}}\right)+32$

Substitute the Fahrenheit temperature in the equation

$114=1.8\left(T_{\mathrm{c}}\right)+32$

$1.8\left(T_{\mathrm{c}}\right)=114-32$

$1.8\left(T_{\mathrm{c}}\right)=82$

$T_{\mathrm{c}}=\frac{82}{1.8}$

$T_{\mathrm{c}}=45°C$

$\cong {46}^{\circ }\mathrm{C}$

Therefore, we have

${114}^{\circ }\mathrm{C}={46}^{\circ }\mathrm{C}$