Question

One end of a conducting rod is maintained at a temperature of 30°C and at the other end, ice is melting at 0°C. The rate of melting of ice is doubled if:

a) The temperature is increased from 30°C to 60°C.

b) The area of the cross-section of the rod is doubled.

c) The area of the cross-section of the rod is made half.

1.

Only a is correct

2.

Only b is correct

3.

Only c is correct

4.

Both a and b are correct

Answer 1

Correct Answer - Option 4 :

Both a and b are correct

CONCEPT:

Conduction:

• The process of transmission of heat energy in which the heat is transferred from one particle of the medium to the other, but each particle of the medium stays at its own position is called conduction.
• The heat transfer rate in conduction is given as,

\(⇒ Q=KA\frac{Δ t}{t}\)

Where Q = transfer of heat per unit time, K = thermal conductivity of the body, A = area of heat transfer, ΔT = temperature difference between the two ends, and t = thickness

EXPLANATION:

• The rate of melting of ice will become double when the heat removing rate becomes double.
• The heat is being removed from the ice with the help of a conducting rod.
• We know that for conduction, the heat transfer rate is given as,

\(⇒ Q=KA\frac{Δ t}{t}\)     -----(1)​

By equation 1,

⇒ Q ∝ A     -----(2)

⇒ Q ∝ Δt     -----(3)

• From equation 2 it is clear that the heat transfer rate will become double when the cross-section of the rod is doubled.
• From equation 3 it is clear that the heat transfer rate will become double when the temperature difference between the two ends is doubled. So when the temperature is increased from 30°C to 60°C, the Δt becomes double, hence the heat transfer rate also becomes double.
• Therefore statement a and statement b are correct.
• Hence, option 4 is correct.