Question

In an external environment of temperature (\(T\)) kelvin, a sphere at temperature (\(3T\)) kelvin has cooling rate \(R_1\). When the temperature of that sphere falls to (\(2T\)) kelvin, the cooling rate \(R_2\) of the sphere will become

• A. \(\frac{15}{16}R_1\)
• B. \(\frac{11}{16}R_1\)
• C. \(\frac{7}{16}R_1\)
• D. \(\frac{3}{16}R_1\)

Hint:

Radiation rate \(\propto T^4-T_0^4\) for a body in surroundings at \(T_0\).

Answer 1

The Correct Option is D

Step 1: Write the two rates
$R_1=k(81-1)T^4$ and $R_2=k(16-1)T^4$.

Step 2: Divide
$R_2/R_1=15/80=3/16$, option (D).

Final Answer:
$R_2=\frac3{16}R_1$, option (D). \[ \boxed{\dfrac{3}{16}R_1} \]