A copper plate and an aluminum plate of equal thickness and area are maintained at the same temperature difference. If the thermal conductivity of copper is twice that of aluminum, what will be the ratio of heat flow through copper to that through aluminum?
The ratio will be 2:1 for copper to aluminum.
To determine the ratio of heat flow through copper to that through aluminum, we will use the formula for heat flow through a material, which is given by the equation:
Q = \frac{{k \cdot A \cdot \Delta T}}{{d}}where:
- Q is the heat flow.
- k is the thermal conductivity of the material.
- A is the cross-sectional area of the plate.
- \Delta T is the temperature difference across the plate.
- d is the thickness of the plate.
We are given that the copper plate and the aluminum plate have equal thickness (d) and area (A), and they are maintained at the same temperature difference (\Delta T). The thermal conductivity of copper is twice that of aluminum, so we have:
- k_{\text{copper}} = 2k_{\text{aluminum}}
Thus, the heat flow for copper and aluminum can be expressed as:
For copper:
Q_{\text{copper}} = \frac{{2k_{\text{aluminum}} \cdot A \cdot \Delta T}}{{d}}For aluminum:
Q_{\text{aluminum}} = \frac{{k_{\text{aluminum}} \cdot A \cdot \Delta T}}{{d}}The ratio of the heat flow through copper to that through aluminum is then:
\frac{{Q_{\text{copper}}}}{{Q_{\text{aluminum}}}} = \frac{{\left(\frac{{2k_{\text{aluminum}} \cdot A \cdot \Delta T}}{{d}}\right)}}{{\left(\frac{{k_{\text{aluminum}} \cdot A \cdot \Delta T}}{{d}}\right)}} = \frac{2k_{\text{aluminum}}}{k_{\text{aluminum}}}This simplifies to:
= 2:1Therefore, the correct answer is that the ratio of heat flow through copper to that through aluminum is 2:1.
Similar Questions
When a hot metal block is placed in a cooler liquid inside a calorimeter, which property of the metal primarily determines how readily heat is conducted through the block to its surface?
Which of the following best explains how the thermal conductivity of a metal rod can be determined experimentally?
Important Questions from Conduction
What is the state, in which none of the properties of the system change with time, known as?
The process of heat transfer from one particle of the body to another without the actual motion of the particle, is known as ______ .
Liquid metal having highest thermal conductivity is of _______.
The transfer of heat through the molecules of matter in any body is called ________.
A hollow cylinder has length L, inner radius r1, outer radius r2 and thermal conductivity K. The thermal resistance of the cylinder for radial conduction is
