Question

One liquid has a temperature of \(140 .{ }^{\circ} \mathrm{F}\) and another liquid has a temperature of \(60.0^{\circ} \mathrm{C}\). Are the liquids at the same temperature or at different temperatures?

Short answer

The liquids are at the same temperature, both are 60.0°C.

Step-by-step solution

Convert Fahrenheit to Celsius

Use the formula to convert from Fahrenheit to Celsius: \[ C = \frac{5}{9} (F - 32) \]Substitute 140°F into the formula:\[ C = \frac{5}{9} (140 - 32) \]Calculate the value inside the parentheses: \[ 140 - 32 = 108 \]Now, multiply by \( \frac{5}{9} \): \[ C = \frac{5}{9} \times 108 = 60.0^{\bullet}\text{C} \]

Compare the Temperatures

Now compare the converted temperature of 140°F, which is 60.0°C, with the given temperature for the second liquid, which is also 60.0°C.

Conclusion

Both converted and given temperatures are the same (60.0°C). Thus, the two liquids are at the same temperature.

Key concepts

Fahrenheit to Celsius conversion

When dealing with temperature, you may need to convert between Fahrenheit and Celsius. For this, there's a handy formula. To convert a temperature from Fahrenheit \text{F} to Celsius \text{C}, use the formula: \( C = \frac{5}{9} (F - 32) \) This formula is crucial for scientific calculations and everyday uses, such as cooking or understanding weather reports from different regions. For example, if you want to convert 140°F to Celsius, you'll first subtract 32 from 140, getting 108. Next, multiply that by \( \frac{5}{9} \), resulting in a temperature of 60.0°C. Understanding this formula helps bridge the gap between these two temperature scales.

temperature comparison

Once you have converted temperatures to the same scale, it's essential to compare them accurately. In our example, after converting 140°F to 60.0°C, you can now compare it directly to the second liquid's temperature of 60.0°C. Here are some quick steps for accurate comparison:

• Ensure both temperatures are in the same unit (either both in Celsius or both in Fahrenheit).
• Use simple arithmetic or logic to determine if one is higher, lower, or equal to the other.

In temperature-sensitive fields such as chemistry or meteorology, proper temperature comparison is vital for accurate results.

temperature equality

Finally, knowing when two temperatures are equal is a fundamental skill. In our problem, after conversion, we saw that both the temperatures were 60.0°C. Here's why understanding temperature equality is important:

• It aids in quality control in industrial processes where maintaining a specific temperature is crucial.
• In cooking, ensuring ingredients are at equal temperatures can affect the outcome of a recipe.
• In scientific experiments, precise temperature measurements and understanding their equality can be crucial for successful results.

Recognizing that our two example liquids are at the same temperature, we concluded that they are equal, which is critical information for subsequent actions or analyses.