MHT CET · Physics · Thermal Properties of Matter
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.
- A the sphere reaches room temperature fast
- B the cube reaches room temperature fast
- C the circular plate reaches room temperature fast
- D all will reach the room temperature simultaneously
Answer & Solution
Correct Answer
(C) the circular plate reaches room temperature fast
Step-by-step Solution
Detailed explanation
\(\rho=\frac{M}{V} \text {; }\)
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.
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.
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