What is the change in length of an aluminum rod after adding 12500 J of energy?

In summary, an aluminum rod with a length of 23.0 cm and a mass of 350 g is heated with 12500 J of energy. Using the equation Q=m*c*delta T, the final temperature of the rod is calculated to be 59.68°C. Using the equation deltaL=alpha*L0*deltaT, the change in length is calculated to be 2.19*10-4 m. However, this answer is incorrect because there was a mistake in the calculation. The correct answer is actually 0.219 mm.
  • #1
ymehuuh
19
0

Homework Statement


An aluminum rod is 23.0 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?

Answer is in mm

Homework Equations


Q=m*c*delta T
deltaL=alpha*L0*deltaT
alpha=24x10^-6
c=900j/kg


The Attempt at a Solution


12500=.35kg*900(Tf-20C)
Tf=59.68

deltaL=24x10^-6*.23m*39.68
The answer I get is 2.19*10-4m which is wrong
That /1000 to get mm is 2.19*10-7 which is wrong

I don't understand what I did wrong...
 
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  • #2
Isn't 2.19*10-4m = .219 mm?
 
  • #3
Whoops...divided instead of multiplied. Thanks.
 

FAQ: What is the change in length of an aluminum rod after adding 12500 J of energy?

1. What is energy?

Energy is the ability to do work or cause change. It exists in many different forms, including heat, light, electricity, and motion.

2. What is thermal expansion?

Thermal expansion is the tendency of matter to change in volume or shape in response to a change in temperature. When a material is heated, its particles vibrate and move more, causing the material to expand. When it is cooled, the particles slow down and the material contracts.

3. How does thermal expansion affect everyday objects?

Thermal expansion can cause everyday objects to change in size or shape when exposed to temperature changes. For example, metal objects can expand and contract when heated and cooled, which can cause them to become loose or tight. This is why bridges have expansion joints to allow for thermal expansion without causing damage.

4. What is the coefficient of thermal expansion?

The coefficient of thermal expansion is a measure of how much a material expands or contracts with a change in temperature. It is typically expressed in units of length per degree Celsius (or Fahrenheit). Different materials have different coefficients of thermal expansion, which can affect how they behave when exposed to temperature changes.

5. How is thermal expansion used in practical applications?

Thermal expansion is used in many practical applications, such as in thermometers, thermostats, and bimetallic strips. It is also important in the design and construction of buildings, bridges, and other structures, as materials need to be able to withstand the effects of thermal expansion without causing damage. Additionally, thermal expansion is utilized in engineering processes such as welding, where the expansion of metal can be used to create strong bonds between pieces.

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