a copper cylinder is initially at 20.0 degree Celsius. At what temperature will its volume be 0.150% larger than it is at 20.0 degree Celsius?
To find the temperature at which the volume of the copper cylinder is 0.150% larger than it is at 20.0 degrees Celsius, we need to use the coefficient of linear expansion for copper and apply it to the initial temperature.
The coefficient of linear expansion (α) for copper is typically given as 0.0000169 per degree Celsius. This means that for every 1 degree Celsius increase in temperature, the linear dimensions of the copper cylinder will increase by 0.0169% of its initial value.
Now, let's calculate the change in volume that corresponds to a 0.150% increase in the linear dimensions.
Given that the volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height, the change in volume (ΔV) can be calculated using the approximation ΔV ≈ 2πrhΔL, where ΔL is the change in length.
Since the length (h) remains constant, we can ignore it for now. The change in length (ΔL) can be calculated using the formula ΔL = αLΔT, where L is the initial length and ΔT is the change in temperature.
Substituting the values, ΔL ≈ (0.0000169 per degree Celsius) * L * ΔT
Since we want ΔL to be 0.150% of the initial length, we have 0.150% = (0.0000169 per degree Celsius) * L * ΔT
Now, solving for ΔT, we have ΔT = 0.150% / [(0.0000169 per degree Celsius) * L]
Substituting the actual values for L, we will get the final answer.
Note: It would be helpful to know the values of the radius (r) and height (h) of the copper cylinder in order to calculate the change in volume accurately.