A square plate of side 15cm is made of linear expansivity 0.00002/k. If the thickness of the plate is 5cm and the plate is heated from 25degree celcius to 30 degree celcius. What is the cubical increase?
What is wrong with
cube Increase= (linear expansivity)*3*change temp
To find the cubical increase, we need to find the change in volume of the square plate.
Given:
Side length of the square plate (l) = 15 cm
Thickness of the plate (t) = 5 cm
Linear expansivity (α) = 0.00002 / K (Kelvin)
Initial temperature (T1) = 25 °C
Final temperature (T2) = 30 °C
Step 1: Find the initial volume of the plate.
The initial volume of the square plate can be calculated as:
Initial Volume (V1) = l^2 * t
= 15 cm * 15 cm * 5 cm
= 1125 cm^3
Step 2: Find the change in temperature.
The change in temperature (ΔT) can be calculated as:
ΔT = T2 - T1
= 30 °C - 25 °C
= 5 °C
Step 3: Calculate the change in length (∆L).
The change in length (∆L) can be calculated using the linear expansivity formula:
∆L = α * L * ΔT
= 0.00002 / K * 15 cm * 5 °C
= 0.0015 cm/K
Step 4: Calculate the final length (L2).
The final length (L2) can be calculated as:
L2 = L1 + ∆L
= 15 cm + 0.0015 cm/K
= 15.0015 cm
Step 5: Calculate the final volume (V2).
The final volume (V2) can be calculated as:
Final Volume (V2) = L2^2 * t
= 15.0015 cm * 15.0015 cm * 5 cm
= 1125.2253 cm^3
Step 6: Calculate the cubical increase (∆V).
The cubical increase (∆V) can be calculated as the difference between the final volume (V2) and the initial volume (V1):
∆V = V2 - V1
= 1125.2253 cm^3 - 1125 cm^3
= 0.2253 cm^3
Therefore, the cubical increase is 0.2253 cm^3.
To find the cubical increase, we need to determine the change in volume of the square plate.
First, we need to calculate the change in length of one side due to the change in temperature. We can use the formula:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length
α is the linear expansivity (0.00002/k in this case)
L0 is the initial length (15cm)
ΔT is the change in temperature (30°C - 25°C = 5°C)
ΔL = 0.00002/k * 15cm * 5°C
ΔL = 0.0015 cm
Since the plate is a square, each side increases by ΔL. Therefore, the total change in each side length is:
ΔL_total = 4 * ΔL
ΔL_total = 4 * 0.0015 cm
ΔL_total = 0.006 cm
Now we can calculate the change in volume. Since the thickness of the plate (height) remains constant, the change in volume is equal to the change in the cross-sectional area, which is the square of the change in side length.
ΔV = (ΔL_total)^2 * h
ΔV = (0.006 cm)^2 * 5 cm
ΔV = 0.00018 cm^3
Therefore, the cubical increase is 0.00018 cm^3.