Thermal Expansion of Cube and Sphere

[frostchaos123]

Homework Statement

A solid sphere and a solid cube are made from the same material. The sphere would just fit within the cube, if it could. Both begin at the same temperature, and both are heated to the same temperature. Which object, if either, has the greatest change in volume?

The answer is the cube.

The Attempt at a Solution

Using the equation for volume expansion, change in V=beta*Vi*change in temperature, shouldn't a higher initial volume give raise to a greater change in volume, therefore the sphere expands more?

 

[epenguin]

Reasoning seem right to me, except if the sphere fits in the cube does the sphere have the higher initial volume?

 

[frostchaos123]

Oops you are right the sphere should have a lesser initial volume, i was assuming that the sphere was bigger than the cube.

Thanks.

 

[epenguin]

Also (I thought afterwards) the answer is a bit more obvious if we don't think of two separate solids. Think of a homogeneous curve of matter. Inside it not physically separate but just delimited in the mind is a sphere touching the cube at 6 points. The whole thing expands. Then you don't have to think so hard to imagine what happens.

 

[rwisz]

Your reasoning is valid, but it overlooks the fact that the cube has a larger surface area than the sphere. This means that the cube is exposed to more heat and will expand more than the sphere. Additionally, the cube has more edges and corners, which are more susceptible to expansion under heat. Therefore, even though the sphere may have a higher initial volume, the cube will experience a greater change in volume due to thermal expansion. This is a common phenomenon observed in real-life applications, such as when constructing buildings or bridges, where materials with a larger surface area are chosen to accommodate for thermal expansion.