At 20°C, a brass cube has an edge length of 34 cm. What is the increase in the cube's surface area when it is heated from 20°C to 67°C?
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To calculate the increase in the cube's surface area when it is heated from 20°C to 67°C, we need to consider the thermal expansion of brass.
The formula to calculate the linear expansion of a material is given by:
ΔL = α * L * ΔT
where ΔL is the change in length, α is the linear expansion coefficient, L is the original length, and ΔT is the change in temperature.
The linear expansion coefficient for brass is typically given as 0.000019 per degree Celsius (0.000019/°C).
First, let's calculate the change in length of one side of the cube:
ΔL = α * L * ΔT
ΔL = 0.000019/°C * 34 cm * (67°C - 20°C)
ΔL = 0.000019/°C * 34 cm * 47°C
ΔL ≈ 0.0302144 cm
Since the cube has six equal sides, the change in surface area can be found by calculating the change in the area of one face and multiplying it by six:
ΔA = 6 * ΔL^2
ΔA = 6 * (0.0302144 cm)^2
ΔA ≈ 0.054996 cm^2
Therefore, the increase in the cube's surface area when it is heated from 20°C to 67°C is approximately 0.055 cm^2.
To find the increase in the cube's surface area, we need to calculate the final surface area at 67°C and then subtract the initial surface area at 20°C.
Let's break down the problem into steps:
Step 1: Calculate the initial surface area.
Given that the edge length of the cube is 34 cm, we can find the initial surface area using the formula:
Initial surface area = 6 * (edge length)^2
So, the initial surface area of the brass cube at 20°C is:
Initial surface area = 6 * (34 cm)^2
Step 2: Calculate the final surface area.
To calculate the final surface area, we need to account for the expansion of the cube due to the change in temperature. The expansion of brass can be calculated using the coefficient of linear expansion.
The linear expansion coefficient for brass is typically given as 19 x 10^-6 per degree Celsius. This means that for every degree Celsius increase in temperature, brass expands by 19 x 10^-6 times its original length.
By multiplying the initial length of the cube's edge by the temperature increase, we can find the increase in length due to thermal expansion:
Increase in length = initial edge length * (temperature change in °C) * coefficient of linear expansion
The final length of the cube's edge can be calculated by adding this increase to the initial length:
Final edge length = initial edge length + increase in length
Now, we can calculate the final surface area using the final edge length:
Final surface area = 6 * (final edge length)^2
Step 3: Calculate the increase in the surface area.
Finally, we can find the increase in surface area by subtracting the initial surface area from the final surface area:
Increase in surface area = Final surface area - Initial surface area
By following these steps and plugging in the given values, you can find the increase in the cube's surface area when heated from 20°C to 67°C
67-20=37°c
34cm=20°c
?cm=37°c
37×34÷20=62.9cm.
SA=6S(squared).
=6(62.9)squared.
=6×3956.41.
SA=23738.46cm squared