Question

The average daytime temperatures on the earth and Jupiter are ${72}^{\circ }\mathrm{F}$ and 313 $\mathrm{K}$ , respectively. Calculate the difference in temperature, in ${}^{\circ }\mathrm{C}$ , between these two planets.

Short answer

The difference in average daytime temperatures between Earth and Jupiter is approximately 17.63°C.

Step-by-step solution

Convert Earth's temperature from Fahrenheit to Celsius

We use the formula to convert Fahrenheit to Celsius: C = (F-32) * (5/9). Given the Earth's average daytime temperature is 72°F, we can calculate the temperature in degrees Celsius as follows: Cₑ = (72-32) * (5/9) = 40 * (5/9) = 200/9 ≈ 22.22°C

Convert Jupiter's temperature from Kelvin to Celsius

The conversion formula from Kelvin to Celsius is C = K - 273.15. Given that Jupiter's average daytime temperature is 313 K, we can calculate the temperature in degrees Celsius: Cⱼ = 313 - 273.15 = 39.85°C

Calculate the difference in temperature between Earth and Jupiter

Now that we have both temperatures in degrees Celsius, we can calculate the difference between them: Temperature Difference = |Cⱼ - Cₑ| = |39.85 - 22.22| = 17.63°C In conclusion, the difference in average daytime temperatures between Earth and Jupiter is approximately 17.63°C.

Key concepts

Fahrenheit to Celsius conversion

Understanding temperature conversion formulas is crucial for scientific calculations, and converting Fahrenheit to Celsius is one of the basics. To convert a temperature from Fahrenheit (°F) to Celsius (°C), you can use the simple formula:

• Subtract 32 from the Fahrenheit temperature.
• Multiply the result by 5/9.

This operation effectively scales the difference from the water freezing and boiling points in the Fahrenheit scale to the Celsius scale. For instance, when converting 72°F, like Earth's average daytime temperature, you perform the calculation: $$C=(72-32)\times \left(\frac{5}{9}\right)=\frac{200}{9}\approx 22.22{}^{\circ }\text{C}$$ This conversion helps standardize temperatures across different regions and scientific documents, making it easier to compare and understand readings from different parts of the world.

Kelvin to Celsius conversion

The Kelvin and Celsius scales are closely related, as they both measure temperature but with different starting points. The Kelvin scale is an absolute thermodynamic scale starting at absolute zero, which is 0 K, while the Celsius scale sets its zero at the freezing point of water. To convert a temperature from Kelvin (K) to Celsius (°C), you simply need to subtract 273.15 from the Kelvin temperature:$$C=K-273.15$$This conversion is rather straightforward. For example, to find the equivalent Celsius temperature of Jupiter's average daytime temperature of 313 K, the calculation is:$$C=313-273.15=39.85{}^{\circ }\text{C}$$This method is useful in scientific studies because Kelvin is often used in physics for its simplicity in calculations involving comfortable measurements from absolute zero. Allowing for an easy conversation to the Celsius scale aids in better communication amongst scientists using different systems.

Temperature difference calculation

Calculating the difference in temperatures between two entities requires both to be in the same unit, ensuring an accurate and meaningful comparison. Once the temperatures of Earth and Jupiter were converted to Celsius, we can directly calculate the difference by subtracting one from the other and taking the absolute value:$$\text{Temperature Difference}=|C_{\text{Jupiter}}-C_{\text{Earth}}|$$Here, with Earth at approximately 22.22°C and Jupiter at 39.85°C, the calculation becomes:$$|39.85-22.22|=17.63{}^{\circ }\text{C}$$This tells us that Jupiter is significantly warmer than Earth on average, during the day, by about 17.63°C. Calculating temperature differences can help in understanding thermal environments, designing equipment for space missions, and assessing climate models across different planets or locations.