A copper rod is 22 mm long at room temperature (20c). What length does it expand to when placed in a 757 degrees Celsius furnace?
To determine the length of the copper rod when placed in a 757 degrees Celsius furnace, we will need to consider the coefficient of linear expansion for copper and the change in temperature.
The coefficient of linear expansion represents how much a material expands per unit length for each degree of temperature change. For copper, the coefficient of linear expansion is approximately 0.000016 per degree Celsius.
First, we need to calculate the change in temperature by subtracting the initial temperature (20 degrees Celsius) from the furnace temperature (757 degrees Celsius):
Change in temperature = 757°C - 20°C = 737°C
Next, we can calculate the change in length using the formula:
Change in length = Coefficient of linear expansion × original length × change in temperature
Change in length = 0.000016/°C × 22 mm × 737°C
Now we can solve for the change in length:
Change in length = 0.000016 × 22 × 737 mm
Finally, to find the length the copper rod expands to, we add the change in length to the original length:
Expanded length = original length + change in length
Expanded length = 22 mm + (0.000016 × 22 × 737) mm
By calculating this equation, we can find the final length of the copper rod when placed in the 757 degrees Celsius furnace.