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Chapter 8: Problem 1087

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

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

Step by step solution

01

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.
02

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.
03

Convert Temperature to Fahrenheit

We need to convert \(4^{\circ} \mathrm{C}\) to Fahrenheit. Plugging the value into the formula, we get: \[F = \frac{9}{5} \times 4 + 32\]
04

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.

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