Question

Consider two solid copper spheres, 1 and 2. Sphere 1 has twice the diameter of sphere 2. If both spheres are initially at 0C and placed in quiescent air at 25 C, which sphere will reach air temperature first?

A. sphere 1
B. sphere 2
C. Both spheres will reach temp at the same time
D. Impossible to tell from the information provided

Answer 1

Sphere 2 will reach air temperature first due to a higher surface area-to-volume ratio, which facilitates faster heat exchange.

Step-by-step explanation:

Considering two solid copper spheres, 1 and 2, where sphere 1 has twice the diameter of sphere 2, the sphere that will reach air temperature first when placed in quiescent air at 25°C from an initial temperature of 0°C is sphere 2, option B. This is due to the sphere's geometry and the rate of heat transfer. In thermodynamics, smaller objects with a higher surface area-to-volume ratio can exchange heat more quickly than larger objects with a lower ratio. Since sphere 2 is smaller, it has a relatively larger surface area-to-volume ratio compared to sphere 1, allowing it to reach thermal equilibrium with its surroundings faster.