Problem 1055 - JEE Physics

Question

Oxygen boils at \(183^{\circ} \mathrm{C}\). This temperature is approximately. (A) \(215^{\circ} \mathrm{F}\) (B) \(-297^{\circ} \mathrm{F}\) (C) \(329^{\circ} \mathrm{F}\) (D) \(361^{\circ} \mathrm{F}\)

Step-by-Step Solution

Answer

The boiling temperature of oxygen is approximately \(329^{\circ}\mathrm{F}\). Therefore, the correct answer is (C).

Step 1: Write down the given temperature in Celsius

The given boiling temperature of oxygen is \(183^{\circ}\mathrm{C}\).

Step 2: Use the Celsius to Fahrenheit conversion formula

We will use the conversion formula where \(F\) is the temperature in Fahrenheit and \(C\) is the temperature in Celsius. \[F = \frac{9}{5} \cdot C + 32\]

Step 3: Substitute the given temperature into the formula

Now, we will substitute \(C = 183^{\circ}\mathrm{C}\) into the formula to find the boiling temperature of oxygen in Fahrenheit. \[ F = \frac{9}{5} \cdot 183 + 32 \]

Step 4: Calculate the boiling temperature in Fahrenheit

Calculation for the Fahrenheit temperature: \[ F = \frac{9}{5} \cdot 183 + 32 = 329.4^{\circ}\mathrm{F} \]

Step 5: Compare the result to the given options

The calculated temperature is approximately \(329.4^{\circ} \mathrm{F}\). Comparing this value to the provided options, we find that the closest value is: (C) \(329^{\circ}\mathrm{F}\) So, the correct answer is (C).

Key Concepts

Celsius to Fahrenheit conversion

Temperature conversion is a fundamental concept in understanding different temperature scales used worldwide. Celsius and Fahrenheit are two common scales. The formula for converting Celsius (°C) to Fahrenheit (°F) is:

• First, multiply the Celsius temperature by \(\frac{9}{5}\).
• Then, add 32 to the result. This accounts for the different starting points of the Fahrenheit scale.

This conversion formula can be expressed as: \[F = \frac{9}{5} \cdot C + 32\]Where:

• \(F\) represents the temperature in Fahrenheit
• \(C\) represents the temperature in Celsius

For example, to convert 100°C (the boiling point of water) to Fahrenheit, you would calculate:\[F = \frac{9}{5} \cdot 100 + 32 = 212°F\]This provides a clear pathway for understanding how to convert any Celsius temperature into the Fahrenheit scale.

Boiling point of oxygen

Oxygen, a crucial element we breathe, turns from liquid to gas at a very low temperature compared to water. The boiling point of oxygen is given as \(183^{\circ} \mathrm{C}\). This is a figure less commonly encountered in daily life because it’s often below the temperature we experience.
However, it’s important in scientific contexts such as in laboratories and various industrial applications. Processing oxygen in its liquid form requires understanding this extremity. This knowledge is vital for handling and storing oxygen safely where fluctuations in its state can dramatically impact processes.
Converting this boiling point to Fahrenheit helps in international communication and comprehension where Fahrenheit is predominantly used.

Fahrenheit temperature calculation

Calculating the Fahrenheit equivalent of a temperature in Celsius involves a straightforward application of the conversion formula. Let’s consider converting the boiling point of oxygen. Given that it boils at \(183^{\circ} \mathrm{C}\), substituting into the formula:

• Multiply 183 by \(\frac{9}{5}\).
• Add 32 to the result to obtain the temperature in Fahrenheit.

Hence, the calculation proceeds as:\[F = \frac{9}{5} \cdot 183 + 32 = 329.4^{\circ}\mathrm{F}\]
This shows how easy it is to find the corresponding Fahrenheit value, which is crucial in verifying scientific data and ensuring accuracy across different temperature scales. Understanding these conversions enables precise communication in scientific, engineering, and daily life scenarios.