A square plate made of copper has a length of 4.253 m on a side, at 15.00 degrees Celsius. A hole is drilled in the plate, the diameter of which is 1.750 m. The plate is heated to 177.00 degrees Celsius. Assume that alpha= 16.8* 10^-6 for copper.

A) calculate the length of a side of the plate at 177.00 degrees Celsius.
B) calculate the new diameter of the hole.

deltaL=coefficient*L*tempchange.

Do I use the same formula for both A and B?

To solve this problem, we can use the concept of thermal expansion.

A) To calculate the length of a side of the plate at 177.00 degrees Celsius, we can use the formula for linear expansion:

ΔL = α * L₀ * ΔT

where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L₀ is the original length, and
ΔT is the change in temperature.

In this case, we want to find the change in length when the temperature changes from 15.00 degrees Celsius to 177.00 degrees Celsius.

First, let's calculate the change in temperature:
ΔT = 177.00 degrees Celsius - 15.00 degrees Celsius = 162.00 degrees Celsius

Now, we can substitute the values into the formula:
ΔL = (16.8 * 10^-6) * (4.253 m) * (162.00 degrees Celsius)

Calculating this, we get:
ΔL = 0.11509272 m

To find the length of a side at 177.00 degrees Celsius, we can add this change in length to the original length:
Length at 177.00 degrees Celsius = Original length + ΔL
Length at 177.00 degrees Celsius = 4.253 m + 0.11509272 m
Length at 177.00 degrees Celsius = 4.36809272 m

So, the length of a side of the plate at 177.00 degrees Celsius is approximately 4.368 m.

B) To calculate the new diameter of the hole, we can use the formula for linear expansion in terms of diameter:

ΔD = 2 * α * D₀ * ΔT

where:
ΔD is the change in diameter,
α is the coefficient of linear expansion,
D₀ is the original diameter, and
ΔT is the change in temperature.

In this case, we want to find the change in diameter when the temperature changes from 15.00 degrees Celsius to 177.00 degrees Celsius.

First, let's calculate the change in temperature:
ΔT = 177.00 degrees Celsius - 15.00 degrees Celsius = 162.00 degrees Celsius

Now, we can substitute the values into the formula:
ΔD = 2 * (16.8 * 10^-6) * (1.750 m) * (162.00 degrees Celsius)

Calculating this, we get:
ΔD = 0.048564 m

To find the new diameter, we can subtract this change in diameter from the original diameter:
New diameter = Original diameter - ΔD
New diameter = 1.750 m - 0.048564 m
New diameter = 1.701436 m

So, the new diameter of the hole at 177.00 degrees Celsius is approximately 1.701 m.