Question

The temperature on Celsius scale is \(25^{\circ} \mathrm{C}\). What is the corresponding temperature on the Fahrenheit Scale? (A) \(40^{\circ} \mathrm{F}\) (B) \(45^{\circ} \mathrm{F}\) (C) \(50^{\circ} \mathrm{F}\) (D) \(77^{\circ} \mathrm{F}\)

Short answer

The corresponding temperature on the Fahrenheit scale is \(77^{\circ} \mathrm{F}\). (D)

Step-by-step solution

Write down the formula to convert Celsius to Fahrenheit

We begin by writing down the formula needed for this conversion: \(F = \frac{9}{5}C + 32\)

Substitute the given value for C

Given that the temperature in Celsius is 25ºC, we replace C with 25 in the formula: \(F = \frac{9}{5}(25) + 32\)

Calculate the temperature in Fahrenheit

Now, we perform the calculations to find the temperature in Fahrenheit: \(F = \frac{9}{5}(25) + 32 = \frac{9(25)}{5} + 32 = 45 + 32\) \(F = 77\)

Find the corresponding answer

With the knowledge that the temperature in Fahrenheit is 77ºF, we look at the answer choices and find that: (D) \(77^{\circ} \mathrm{F}\) So, the correct answer for the problem is choice (D).

Key concepts

Celsius to Fahrenheit

Converting temperatures from Celsius to Fahrenheit might seem tricky at first, but it becomes easy with the right approach. The Celsius scale, also referred to as the centigrade scale, is one of the most commonly used scales worldwide to measure temperature. On the other hand, the Fahrenheit scale is primarily used in the United States.
To convert a temperature from Celsius to Fahrenheit, you use a simple step-by-step formula that helps in obtaining the temperature reading on the Fahrenheit scale accurately. The decision whether to convert temperatures largely depends on the context; international travelers or people dealing with global data often need to switch between these scales.

Measurement Scales

The Celsius and Fahrenheit scales are both valuable tools for measuring temperature, but they have their unique histories and uses.

• Celsius Scale: Invented by Anders Celsius in the 18th century, this scale is based around the freezing and boiling points of water, at 0°C and 100°C respectively.
• Fahrenheit Scale: Developed by Daniel Gabriel Fahrenheit, it uses the freezing point of water at 32°F and the boiling point at 212°F.

These scales provide different perspectives, especially in fields like meteorology, physics, and everyday weather forecasting. Understanding the difference is key to making correct conversions and interpretations. Although Fahrenheit might be less intuitive for some, it allows for a greater detailed reading due to its larger range per unit compared to Celsius.

Conversion Formula

The conversion formula from Celsius to Fahrenheit is straightforward and essential for transforming temperatures between the two units. The formula is:\[ F = \frac{9}{5}C + 32 \]Here's a breakdown of what this formula does:

• Multiplies the Celsius temperature by \(\frac{9}{5}\) (or 1.8). This step scales the reading to align with the Fahrenheit measurements.
• Adds 32 to the product. This accounts for the difference in where the two scales set their zero points (freezing point).

By understanding each part of this formula, the conversion process becomes clearer. Remember, practicing with different values helps solidify your grasp of these operations and improves your calculation speed and confidence.

Physics Problem Solving

Physics problem solving requires a good understanding of different concepts, including measurement and conversion. When addressing problems, following a structured approach helps greatly.

Step-by-Step Approach

Consider the given problem, identify what is being asked, and determine what data (such as temperature) is provided.

• Write down the appropriate formula, as seen in this exercise with the Celsius to Fahrenheit conversion.
• Substitute the known values into the equation.
• Carry out calculations carefully to avoid errors.
• Check your result against possible choices to ensure accuracy.

This organized strategy helps you systematically tackle not only temperature conversion problems but various other physics-related tasks, improving both accuracy and efficiency.