When exposed to sunlight, a hole in a sheet of copper expands in diameter by 0.154% compared to its diameter at 74∘F.
Part A
What is the Celsius temperature of the copper sheet in the sun?
To find the Celsius temperature of the copper sheet in the sun, we can use the given information and the formula for converting between Celsius and Fahrenheit temperatures:
°C = (°F - 32) * 5/9
Let's first find the change in temperature in Fahrenheit by multiplying the change in diameter by the original diameter at 74°F. We can then add this change to the original temperature of 74°F to find the final temperature in Fahrenheit.
Change in diameter = 0.154% = 0.154/100 = 0.00154
Original diameter = 74°F
Change in temperature in Fahrenheit = Change in diameter * Original diameter = 0.00154 * 74°F
= 0.11396°F
Final temperature in Fahrenheit = Original temperature + Change in temperature
= 74°F + 0.11396°F
= 74.11396°F
Now, let's convert the temperature from Fahrenheit to Celsius using the formula mentioned above:
°C = (°F - 32) * 5/9
°C = (74.11396 - 32) * 5/9
°C = 42.11396 * 5/9
°C = 23.39664
Therefore, the Celsius temperature of the copper sheet in the sun is approximately 23.40°C.