Question

Two vessels of different materials are similar in every respect. The same quantity of ice filled in them gets melted in 25 minutes and 50 minutes respectively. Ratio of their thermal conductivities is: 

1. 3 ∶ 4 
2. 2 ∶ 1
3. 1 ∶ 2
4. 2 ∶ 5

Answer 1

Correct Answer - Option 2 : 2 ∶ 1

CONCEPT:

• Thermal conductivity: It is defined as the property of a given material to transfer heat energy.

It is given by:

 \(k = \frac{QL}{AΔ T}\)

Where k is the thermal conductivity (Wm-1K-1), Q is the amount of heat transferred through the material (W), L is the length between two points of the material (m), A is the cross-sectional area perpendicular to heat flow (m2), and ΔT is the change in temperature (K).

CALCULATIONS:

Given that, T₁ = 25 min, T₂ = 50 min

As from the above formula

\(k = \frac{QL}{AΔ T}\)

Here, the material is different and the quantity is the same

k α 1/T and all other parameters are constant

\(\frac{k_1}{k_2}=\frac{\Delta T_2}{\Delta T_1}=\frac{50}{25}=\frac{2}{1}\)

So the ratio of thermal conductivity is 2:1