Question

At Which temperature the density of water is maximum? (A) \(4^{\circ} \mathrm{F}\) (B) \(42^{\circ} \mathrm{F}\) (C) \(32^{\circ} \mathrm{F}\) (D) \(39.2^{\circ} \mathrm{F}\)

Short answer

The density of water is maximum at \(39.2^{\circ} \mathrm{F}\).

Step-by-step solution

Fact Recall

The density of water is known to be at its maximum at a temperature of \(4^{\circ} \mathrm{C}\) (degrees Celsius). However, the given options are in degrees Fahrenheit. Hence, we need to convert this temperature from Celsius to Fahrenheit.

Temperature Conversion Formula

To convert the temperature from Celsius to Fahrenheit, we can use the following formula: \[F = \frac{9}{5} \times C + 32\] Here, F denotes the temperature in Fahrenheit, and C denotes the temperature in Celsius.

Convert Temperature to Fahrenheit

We need to convert \(4^{\circ} \mathrm{C}\) to Fahrenheit. Plugging the value into the formula, we get: \[F = \frac{9}{5} \times 4 + 32\]

Calculate the Temperature

To find the answer, we need to perform the calculations. \begin{align*} F &= \frac{9}{5} \times 4 + 32 \\ &= \frac{9 \times 4}{5} + 32 \\ &= \frac{36}{5} + 32 \\ & = 7.2 + 32 \\ & = 39.2 \end{align*} Hence, the density of water is maximum at \(39.2^{\circ} \mathrm{F}\) which corresponds to (D) as our correct answer.

Key concepts

temperature conversion

Understanding how to convert temperatures between different units is essential, especially in scientific contexts. Temperature conversion allows us to interpret measurements consistently, no matter the scale used. Many countries using the metric system measure temperature in degrees Celsius (\(^{\circ}C\), while the United States commonly uses degrees Fahrenheit (\(^{\circ}F\). These conversions are crucial for fields like meteorology, cooking, and chemistry.

Here’s a quick guide on how to convert temperatures:

• To convert from Celsius to Fahrenheit, use the formula: \[ F = \frac{9}{5} \times C + 32 \]
• The formula for converting Fahrenheit to Celsius is: \[ C = \frac{5}{9} \times (F - 32) \]

Understanding these formulas is essential, as it enables you to easily switch between temperature units based on your needs. Let's explore how this relates to water density.

maximum density of water

Water behaves uniquely compared to many substances when heated or cooled. Its density—that is, mass per unit volume—does not increase uniformly like metals or other common materials. Instead, water reaches its maximum density at a specific temperature, about \(4^{\circ}C\). Maximal density in water means that its molecules are most closely packed together.

This is because, below \(4^{\circ}C\), water begins to expand due to the formation of a crystalline structure as it approaches the freezing point. This characteristic is vital for aquatic life, preventing bodies of water from freezing solid from the bottom up, as ice—being less dense—floats.
Understanding water's density behavior helps explain natural phenomena and is essential for fields like environmental science and engineering.

Celsius to Fahrenheit conversion

In scientific problems, you often need to convert temperatures from Celsius to Fahrenheit. We explored earlier the formula used for this conversion which is: \[ F = \frac{9}{5} \times C + 32 \]

For instance, converting \(4^{\circ}C\)—where water density is maximal—into Fahrenheit, involves plugging the value into this formula: \[ F = \frac{9}{5} \times 4 + 32 \]
Calculating results in a temperature of \(39.2^{\circ}F\).
This knowledge is not only useful in solving academic exercises but is also applicable in real-life scenarios. For example, understanding these conversions assists in food preparation and weather-related decisions for activities.

basic physics problem solving

Approaching physics problems systematically enhances understanding and success. Here's a simple guide to tackling physics questions, like the one dealing with water density and temperature conversion.

• Identify what's being asked: Focus on the goal. In our exercise, it's finding the temperature where water's density is highest.
• Fact recall: Use known facts, such as water being densest at \(4^{\circ}C\).
• Apply formulas: Convert units using appropriate formulas. For example, the problem required converting Celsius to Fahrenheit.
• Perform calculations: Execute calculations carefully to ensure accuracy.

Problems like these help develop critical thinking and problem-solving skills, essential for physics and other scientific studies.