A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to…

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of $200^{\circ} \mathrm{C}$. When these are left in a room.
  1. the sphere reaches room temperature fast
  2. the cube reaches room temperature fast
  3. the circular plate reaches room temperature fast
  4. all will reach the room temperature simultaneously

Solution

$\rho=\frac{M}{V} \text {; }$ Given: three objects are' of same materials $\rho$ is same. Also, $\mathrm{M}=$ same, $\therefore \quad$ volume of objects is samé. For constant volume, amongst the given objects surface area of the plate is maximum. Hence according to Stefan's law $\frac{\mathrm{dQ}}{\mathrm{dt}} \propto \mathrm{AT}^4$ As $A_{\text {plate }}$ is maximum, the plate will cool fastest and reaches room temeperature fast.

Asked in: MHT CET 2023 (14 May Shift 1)

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