Question

One end of a conducting rod is maintained at temperature 50°C and at the other end ice is maintained at 0°C. The rate of melting of ice is doubled if –

• A. The temperature is made 200⁰C and the area of cross-section of the rod is doubled
• B. The temperature is made 100⁰C and length of the rod is made four times
• C. Area of cross-section of the rod is halved and length is doubled
• D. The temperature is made 100⁰C and area of cross-section of rod and length both are doubled

Answer 1

Answer: (D)

The temperature is made 100⁰C and area of cross-section of rod and length both are doubled

Answer 2

Rate of melting of ice µ rate of heat transfer $\left( \frac{dQ}{dt} \right)$

further, $\frac{dQ}{dt}$ = $\frac{temperaturedifference}{(\mathcal{l}/KA)}$

or $\frac{dQ}{dt}$ µ $\frac{tempdiff}{\mathcal{l}}$ × A

If temp. diff, A and l are all doubled, then dQ and hence rate of melting of ice are doubled