Question

1. carry out the indicated temperature conversions: a. -153 °f to kelvins (k) b. -153 °c to kelvins (k) c. 555 °c to fahrenheit degrees d. -24 °f to celsius degrees

Explanation:

Step1: Recall Fahrenheit - Kelvin conversion formula

$K=\frac{5}{9}(F - 32)+273.15$
For $F=- 153^{\circ}F$, substitute into the formula:
$K=\frac{5}{9}(-153 - 32)+273.15$

Step2: Calculate the value inside the parentheses

$-153-32=-185$
So, $K=\frac{5}{9}\times(-185)+273.15$

Step3: Calculate $\frac{5}{9}\times(-185)$

$\frac{5}{9}\times(-185)=-\frac{925}{9}\approx - 102.78$

Step4: Calculate the final value of $K$

$K=-102.78 + 273.15=170.37\approx170.4$ K

Step5: Recall Celsius - Kelvin conversion formula

$K = C+273.15$
For $C=-153^{\circ}C$, substitute into the formula:
$K=-153 + 273.15 = 120.15\approx120.2$ K

Step6: Recall Celsius - Fahrenheit conversion formula

$F=\frac{9}{5}C + 32$
For $C = 555^{\circ}C$, substitute into the formula:
$F=\frac{9}{5}\times555+32$

Step7: Calculate $\frac{9}{5}\times555$

$\frac{9}{5}\times555 = 9\times111=999$

Step8: Calculate the final value of $F$

$F=999+32 = 1031^{\circ}F$

Step9: Recall Fahrenheit - Celsius conversion formula

$C=\frac{5}{9}(F - 32)$
For $F=-24^{\circ}F$, substitute into the formula:
$C=\frac{5}{9}(-24 - 32)$

Step10: Calculate the value inside the parentheses

$-24-32=-56$
So, $C=\frac{5}{9}\times(-56)=-\frac{280}{9}\approx - 31.1^{\circ}C$

Answer:

a. $170.4$ K
b. $120.2$ K
c. $1031^{\circ}F$
d. $-31.1^{\circ}C$