Which cools faster, a cube or sphere of equal volume?

[campa]

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

 

[quasi426]

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.

 

[kleinwolf]

I thought it was exactly the opposite : round shapes have the maximum containance (volume resp. surface) at equal containing (surface resp. perimeter)...??

 

[whozum]

For a spherical shape, the volume to surface area relation simplifies to

$$\frac{\frac{4}{3}\pi r^3}{4\pi r^2} = \frac{r}{3}$$

A cubic:

$$\frac{8R^3}{24R^2} = \frac{R}{3}$$

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