a copper cylinder has a radius of 2.5 cm and a length of 5.6 cm at 20 degree Celsius. The rod is heated until its temperature is 85 degree Celsius. Find the density at 85 degree Celsius.
87 kg/cubic meters
Problem solving??
Solving pls!!!
To find the density of the copper cylinder at 85 degrees Celsius, we can follow these steps:
Step 1: Find the initial volume of the copper cylinder
The volume of a cylinder can be calculated using the formula V = πr^2h, where
- V is the volume,
- π is approximately 3.14159 (pi),
- r is the radius of the cylinder, and
- h is the height (length) of the cylinder.
Given:
- Radius (r) = 2.5 cm
- Length (h) = 5.6 cm
Using the formula, we can calculate the initial volume (V_initial) of the copper cylinder at 20 degrees Celsius:
V_initial = π * (2.5 cm)^2 * 5.6 cm
Step 2: Calculate the change in volume
When an object is heated or cooled, it undergoes thermal expansion or contraction. The change in volume (ΔV) can be calculated using the formula:
ΔV = V_initial * β * ΔT
Where:
- ΔV is the change in volume,
- V_initial is the initial volume,
- β is the coefficient of volumetric expansion of the material (copper in this case), and
- ΔT is the change in temperature (final temperature - initial temperature).
Given:
- Final temperature = 85 degrees Celsius
- Initial temperature = 20 degrees Celsius
We need the coefficient of volumetric expansion (β) for copper. The coefficient of volumetric expansion for most materials is readily available in reference books or online. For copper, the coefficient of volumetric expansion is approximately 0.0000163 per degree Celsius.
Using the formula, we can calculate the change in volume (ΔV):
ΔV = V_initial * β * ΔT
Step 3: Find the final volume
The final volume (V_final) of the copper cylinder at 85 degrees Celsius is given by:
V_final = V_initial + ΔV
Step 4: Calculate the density
Density (ρ) is defined as the mass (m) divided by the volume (V), so we can calculate the density of the cylinder at 85 degrees Celsius using the formula:
Density (ρ) = mass (m) / V_final
To find the mass (m), we need to use the density of copper at a standard temperature, typically 20 degrees Celsius. The density of copper at 20 degrees Celsius is approximately 8.96 grams per cubic centimeter (g/cm³). Since the volume is in cubic centimeters (cm³), the result will be in grams (g).
Step 5: Calculate the mass
Mass (m) = Density at 20°C * V_initial
Step 6: Calculate the density at 85 degrees Celsius
Density at 85°C = Mass / V_final
By following these steps and the given parameters, you can calculate the density of the copper cylinder at 85 degrees Celsius.