Thermal properties of matter caluculation

In summary, the temperature rise can be calculated using the equation heat energy = mass x shc x temperature change, where the change in velocity is equal to the change in specific momentum and the change in energy is equal to the change in kinetic energy. Knowing the specific kinetic energy and specific heat allows for the elimination of mass in the equation.
  • #1
exotic rooftile
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A squash ball of mass 46g is struck against a wall so it hits with a speed of 40m/s, and rebounds with a speed of 25m/s.
Calculate the temperature rise (s.h.c. of rubber is 1600J/kg/K)

This is fine. I use the equation:

heat energy = mass x shc x temperature change

(40 - 25) = 0.046 x 1600 x temperature change

15/73.6 = temperature change

temperature change = 0.2K

Then it asks why is it unecessary to know the mass?

And I cannot for the life of me think why. Is there another equation I'm supposed to know? Have I made a mistake? Am I overlooking something incredibly obvious?

Any help/hints would be very much appreciated.

Thanks,
Rachael
 
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  • #2
This is fine. I use the equation:

heat energy = mass x shc x temperature change

(40 - 25) = 0.046 x 1600 x temperature change

15/73.6 = temperature change

temperature change = 0.2K
The part of the solution (40-25) is not the heat energy. It's best to write units with the corresponding values.

The 40 m/s - 25 m/s is simply the change in velocity (which is also the change in specific momentum). The change in energy is the change in kinetic energy and KE = 1/2 mv2. But looking at the righthand side one multiplies the mass * specific heat.

If we deal with the specific kinetic energy and specific heat, we can eliminate mass from the equation. Thus

[itex]\Delta[/itex]v2/2 = shc*[itex]\Delta[/itex]T
 
  • #3


It is unnecessary to know the mass because the heat energy is directly proportional to the mass and the specific heat capacity. As long as the mass remains constant, the temperature rise will also remain constant regardless of the mass. Therefore, the mass is not a necessary factor in this calculation.
 

1. What are thermal properties of matter?

Thermal properties of matter refer to the characteristics of a material that determine how it responds to changes in temperature, such as its specific heat capacity, thermal conductivity, and thermal expansion.

2. How do you calculate specific heat capacity?

Specific heat capacity is calculated by dividing the amount of heat energy transferred to an object by its mass and the change in temperature. The unit for specific heat capacity is J/kg·K.

3. What is thermal conductivity?

Thermal conductivity is a measure of how well a material can conduct heat. It is defined as the amount of heat energy that can pass through a unit area of a material in a unit of time, with a unit temperature difference. The unit for thermal conductivity is W/m·K.

4. How does thermal expansion affect matter?

Thermal expansion is the tendency of matter to change in volume or dimensions in response to a change in temperature. This can result in expansion or contraction of a material, which can have practical applications in areas such as construction and engineering.

5. Can thermal properties of matter change?

Yes, thermal properties of matter can change depending on factors such as temperature, pressure, and chemical composition. For example, the thermal conductivity of a material may increase with increasing temperature, or the specific heat capacity may vary depending on the phase of the material.

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