An aluminum rod is 21.5 cm long at 20°C and has a mass of 350 g. If 12500 J of energy is added to the rod by heat, what is the change in length of the rod?

first find the change in temp

heat=mass*specificHeat*deltaTemp

look up specificheat for al, compute delta temp

then, go to linear expansion.
deltaLength= Length*coefflinearexpansion*deltaTemp
look up the linear expansion coeff, compute change in length.

It's very good but just only need the accurate procedures

Well, it seems like that aluminum rod couldn't handle the heat and decided to stretch out a bit! Let's see how much it grew.

We can use the coefficient of linear expansion for aluminum to find the change in length. The coefficient of linear expansion for aluminum is about 0.000022 per degree Celsius.

Now, for the math part! Since we're given the initial length of the rod at 20°C, we can calculate the change in length using the formula:

ΔL = α * L * ΔT

Where ΔL is the change in length, α is the coefficient of linear expansion, L is the initial length, and ΔT is the change in temperature.

Plugging in the given values, we get:

ΔL = 0.000022 * 21.5 cm * ΔT

But we need to convert the mass into energy, just for fun! So, let's calculate the specific heat capacity of aluminum:

specific heat capacity = (energy added) / (mass * ΔT)

Plugging in the given values, we get:

specific heat capacity = 12500 J / (350 g * ΔT)

Now let's set these two expressions equal to each other and solve for ΔT:

0.000022 * 21.5 cm * ΔT = 12500 J / (350 g * ΔT)

Well, my calculations seem to be taking a bit longer than expected! Let me just call my mathematician friend to help me out.

To find the change in length of the aluminum rod, we can use the linear thermal expansion equation:

ΔL = α * L * ΔT

where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length of the rod
ΔT is the change in temperature

First, let's calculate the change in temperature:

ΔT = final temperature - initial temperature

Next, we need to find the coefficient of linear expansion for aluminum. The coefficient of linear expansion for aluminum is approximately 0.000022/°C.

Now, let's calculate the change in length using the formula:

ΔL = α * L * ΔT

Substituting the given values into the formula:

ΔL = (0.000022/°C) * 21.5 cm * ΔT

Finally, we need to convert the change in length from centimeters to meters:

ΔL (m) = ΔL (cm) / 100

Now we are ready to calculate the change in length of the aluminum rod. Please provide the final temperature.

To calculate the change in length of the aluminum rod, we need to use the concept of thermal expansion. The change in length of an object due to temperature changes can be calculated using the coefficient of linear expansion.

The coefficient of linear expansion (α) for aluminum is given as 0.000022/°C. This means that for every degree Celsius change in temperature, the length of the aluminum rod will change by 0.000022 times its original length.

Given:
Initial length (L₁) = 21.5 cm
Change in temperature (ΔT) = final temperature - initial temperature = Tf - Ti

First, let's convert the initial length from centimeters to meters:
L₁ = 21.5 cm = 0.215 m

Next, let's calculate the change in length of the rod due to the change in temperature using the formula:
ΔL = α * L₁ * ΔT

Substituting the values:
ΔL = 0.000022 * 0.215 * ΔT

To find the change in temperature, we need to use the equation that relates heat (Q) to the mass, specific heat capacity (c), and the change in temperature:
Q = mcΔT

Given:
Heat added (Q) = 12500 J
Mass (m) = 350 g = 0.35 kg
Specific heat capacity (c) for aluminum = 900 J/kg°C

Rearranging the equation to solve for ΔT:
ΔT = Q / (mc)

Now, substitute the given values:
ΔT = 12500 J / (0.35 kg * 900 J/kg°C)

Simplify:
ΔT = 12500 / (0.35 * 900) °C

Now, substitute ΔT back into the equation for ΔL:
ΔL = 0.000022 * 0.215 * ΔT

Calculate:
ΔL = 0.000022 * 0.215 * (12500 / (0.35 * 900))

Simplify:
ΔL = 0.000022 * 0.215 * 50 / 9

Finally, calculate the change in length:
ΔL ≈ 0.0000267 meters (or 0.0267 mm)

Therefore, the change in length of the aluminum rod, when 12500 J of energy is added to it, is approximately 0.0000267 meters (or 0.0267 mm).