Problem 79 - Chemistry The Science in Context

Question

Radiator Coolant The coolant in an automobile radiator freezes at \(-39^{\circ} \mathrm{C}\) and boils at \(110^{\circ} \mathrm{C} .\) What are these temperatures on the Fahrenheit scale?

Step-by-Step Solution

Answer

Answer: The freezing point of the radiator coolant in Fahrenheit is -38.2°F, and the boiling point is 230°F.

Step 1: Convert the freezing point to Fahrenheit

We will use the conversion formula for the freezing point of the coolant. Given °C = -39, let's find the temperature in °F. °F = (-39 × 9/5) + 32

Step 2: Calculate the freezing point in Fahrenheit

Now we will perform the calculations. °F = (-39 × 9/5) + 32 °F = (-351/5) + 32 °F = -70.2 + 32 °F = -38.2 So, the freezing point of the radiator coolant in Fahrenheit is -38.2°F.

Step 3: Convert the boiling point to Fahrenheit

We will use the conversion formula for the boiling point of the coolant. Given °C = 110, let's find the temperature in °F. °F = (110 × 9/5) + 32

Step 4: Calculate the boiling point in Fahrenheit

Now we will perform the calculations. °F = (110 × 9/5) + 32 °F = (990/5) + 32 °F = 198 + 32 °F = 230 So, the boiling point of the radiator coolant in Fahrenheit is 230°F.

Key Concepts

Celsius to Fahrenheit

Temperature conversion between Celsius and Fahrenheit is a common task, especially in fields like science and engineering.
One of the most important formulas for conversion is:

• \( \text{°F} = \left( \text{°C} \times \frac{9}{5} \right) + 32 \)

This formula converts a temperature from Celsius (°C) to Fahrenheit (°F).
Let's break it down:- Multiply the Celsius value by \( \frac{9}{5} \) (or 1.8).- Then, add 32 to this result.
This method allows you to convert any Celsius value to its equivalent in Fahrenheit easily. Used in the provided exercise, this formula translates the answer we need by using simple algebra.

Freezing Point

The freezing point is the temperature at which a liquid turns into a solid.
For water, this is 0°C in Celsius and 32°F in Fahrenheit. However, different substances have different freezing points. In the example of radiator coolant, the freezing point is well below that of water, at \(-39^{\circ} \text{C}\).

• The formula to convert this to Fahrenheit is \( \text{°F} = \left(-39 \times \frac{9}{5} \right) + 32 \).
• After doing the math: \(-70.2 + 32 \) results in a freezing point of \(-38.2^{\circ} \text{F}\).

This conversion is crucial in understanding how substances behave in cold environments. With these calculations, automotive engineers know the coolant will stay liquid even at extremely low temperatures.

Boiling Point

The boiling point is the temperature at which a liquid becomes a gas.
For water, this is 100°C or 212°F, but radiator coolant is designed to withstand much higher temperatures, boiling at 110°C.

• We convert this to Fahrenheit using the formula \( \text{°F} = \left(110 \times \frac{9}{5} \right) + 32 \).
• Calculating gives us a Fahrenheit boiling point of \(198 + 32\), which equals \(230^{\circ} \text{F}\).

Knowing the boiling point helps ensure that the coolant can function effectively without vaporizing in the high temperatures generated by an engine. This ensures engine efficiency and safety.