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Law Of Thermal Conductivity MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Law of Thermal Conductivity is considered one of the most asked concept.

  • 11 Questions around this concept.

Solve by difficulty

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time t?

Concepts Covered - 1

Law of Thermal Conductivity

Law of Thermal Conductivity - 

 

                                          

Consider a rod of length 'l' , area of cross-section 'A' whose faces are maintained at temperature \theta_1 and \theta_2 respectively. In steady state the amount of heat flowing from one face to the other face in time t is given by - 

                                                            Q=\frac{K A\left(\theta_{1}-\theta_{2}\right) t}{l}

                                              \\ Q = Amount \ of \ heat\ transfer \\ t = Time \ of\ heat \ flow \\ K = Thermal \ conductivity \ of \ the \ material

 

So, from the above equation we can calculate the -  Rate of flow of heat i.e. heat current which can be written as - 

                                                             \frac{Q}{t}=H=\frac{K A\left(\theta_{1}-\theta_{2}\right)}{l}

In the differential form, this heat current can also be written as - 

                                                                  \frac{d Q}{d t}=-K A \frac{d \theta}{d x}

In case of non-steady state or variable cross-section, this is the more general equation can be used to solve problems.

 

Relation of thermal conductivity of some material - 

                                                         \begin{array}{l}{K_{A g}>K_{C u}>K_{A l}} \\ {K_{S o li d}>K_{L iq u i d }>K_{G a s}} \\ {K_{M e t a l s}>K_{N o n-m e t a l s}}\end{array}

Thermal resistance (Rth) : The thermal resistance of a body is defined as the measure of its opposition to the flow of heat through it. It is defined as the ratio of temperature difference to the heat current(\frac{Q}{t})

                                            R_{th}=\frac{\theta_{1}-\theta_{2}}{H}=\frac{\theta_{1}-\theta_{2}}{K A\left(\theta_{1}-\theta_{2}\right) / I}=\frac{l}{K A}

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Law of Thermal Conductivity

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