Chapter A1, Problem 1E

Convert each temperature.
a. 32 ⁰F to ⁰C (temperature at which water freezes)
b. 77 K to ⁰F (temperature of liquid nitrogen)
c. -109 ⁰F to ⁰C (temperature of dry ice)
d. 98.6 ⁰F to K (body temperature)

Interpretation Introduction

To convert: The given temperature into the required units

Explanation of Solution

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

The equation used to relate ^oF and ^oC is given as follows:

$T(°C)=\frac{T(°F)-32}{1.8}$

Step 1: Substitute the temperature given:

$T(°C)=\frac{T(°F)-32}{1.8}$

Step 2: Calculate Temperature

$\begin{array}{l}T(°C)=\frac{32-32}{1.8}=\frac{0}{1.8}\\ T(°C)=0°C\end{array}$

Interpretation Introduction

To convert: The given temperature into the required units

Explanation of Solution

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

The equation used to relate ^oF with ^oC and K with ^oC is given as follows:

$\begin{array}{l}T(°F)=1.8\cdot T(°C)+32\\ T(K)=T(°C)+273.15\end{array}$

Step 1: Substitute the temperature given:

$T(°C)=T(K)+273.15$

Step 2: Calculate Temperature in °C

$\begin{array}{l}T(°C)=77-273.15\\ T(°C)=\text{-196}\text{.15°C}\end{array}$

Step 3: Calculate °F

$T(°F)=1.8\cdot T(°C)+32$

$\begin{array}{l}T(°F)=1.8\cdot (\text{-196}\text{.15°C})+32\\ T(°F)=-321.07°F\end{array}$

Interpretation Introduction

To convert: the given temperature into the required units

Explanation of Solution

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

The equation used to relate ^oF with ^oC is given as follows:

$T(°C)=\frac{T(°F)-32}{1.8}$

Step 1: Substitute the temperature given:

$T(°C)=\frac{T(°F)-32}{1.8}$

Step 2: Calculate Temperature

$\begin{array}{l}T(°C)=\frac{-109-32}{1.8}=\frac{-141}{1.8}\\ T(°C)=-78.33°C\end{array}$

Interpretation Introduction

To convert: the given temperature into the required units

Explanation of Solution

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

The equation used to relate ^oF with ^oC is given as follows:

$T(°C)=\frac{T(°F)-32}{1.8}$

Step 1: Substitute the temperature given:

$T(°C)=\frac{T(°F)-32}{1.8}$

Step 2: Calculate Temperature

$\begin{array}{l}T(°C)=\frac{98.6-32}{1.8}\\ T(°C)=37°C\end{array}$

Step 3: Calculate absolute temperature

$\begin{array}{l}T(K)=T(°C)+273.15\\ T(K)=37+273.15\\ T(K)=310.15K\end{array}$

Conclusion

$\begin{array}{l}\text{a}\text{.}\text{0 °C}\\ \text{b}\text{.}\text{-321}\text{.07 °F}\\ \text{c}\text{.}\text{-78}\text{.33 °C}\\ \text{d}\text{. 310}\text{.15 K}\end{array}$