Comparing dQ/dt & dT/dt of a Cube & a Globe

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In summary, the rate of change of energy/temperature is greater for an object with a smaller surface area. In this case, the cube would have a higher dQ/dt and dT/dt compared to the globular object due to its smaller surface area. This can be observed by setting the volumes of both objects equal to each other and comparing their surface areas.
  • #1
campa
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If there is a globular object and cube which have the same volume and you heat both of these objects in same amounts of heat and leave these to cool down
1)dQ/dt of which one is higher? If so why?
2)dT/dt of which one is higher? if so why?
t-time
Q-energy
T-temperature
 
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  • #2
Assuming both objects have the same material properties then the greater the surface area the greater the rate of change of energy/temperature. The cube will have a smaller surface area than then globular object, let's say a sphere. You can prove this by setting the volumes equal to each other, make both volumes in terms of one parameter like the radius of the sphere or the length of the cube. Then you can determine the surface areas of both and compare.
 
  • #3
I thought it was exactly the opposite : round shapes have the maximum containance (volume resp. surface) at equal containing (surface resp. perimeter)...??
 
  • #4
For a spherical shape, the volume to surface area relation simplifies to

[tex] \frac{\frac{4}{3}\pi r^3}{4\pi r^2} = \frac{r}{3}[/tex]

A cubic:

[tex] \frac{8R^3}{24R^2} = \frac{R}{3}[/tex]

Note for the same volume [itex] R > r [/itex] in all cases so I believe the cube would dissipate heat faster.
 

Related to Comparing dQ/dt & dT/dt of a Cube & a Globe

What is the difference between dQ/dt and dT/dt?

dQ/dt and dT/dt are both rates of change, but they measure different things. dQ/dt measures the rate of change of heat, while dT/dt measures the rate of change of temperature.

Why is it important to compare dQ/dt and dT/dt of a cube and a globe?

Comparing dQ/dt and dT/dt of a cube and a globe can help us understand how different shapes and materials affect heat transfer. This information can be useful in designing and improving insulation, heating/cooling systems, and other technologies that involve heat exchange.

How do the shapes of a cube and a globe affect their dQ/dt and dT/dt?

The shape of an object can affect its surface area and volume, which in turn can affect its dQ/dt and dT/dt. A cube has a larger surface area compared to a sphere of the same volume, so it can transfer heat more quickly. However, a sphere has a more compact volume, which means it can retain heat better and have a slower dT/dt compared to a cube.

Which one, dQ/dt or dT/dt, is a more accurate measure of heat transfer?

Neither dQ/dt nor dT/dt is more accurate than the other. They both measure different aspects of heat transfer and can be useful in different situations. For example, dQ/dt can tell us how quickly heat is being transferred from one object to another, while dT/dt can tell us how quickly the temperature of an object is changing over time.

What other factors can affect dQ/dt and dT/dt besides shape and material?

Other factors that can affect dQ/dt and dT/dt include the temperature difference between two objects, the type of heat transfer (conduction, convection, or radiation), and the presence of any insulating materials. Additionally, the environment and external factors such as wind, humidity, and pressure can also affect heat transfer and temperature change.

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