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Engineering physics 4(Thermal conductivity)
This document contains lecture notes from Mr. Gouri Kumar Sahu on Engineering Physics. It covers session 5 which includes topics on thermal conductivity, the expression for thermal conductivity, and the Wiedemann-Franz law. Key points include the definition of thermal conductivity as the ratio of heat flow to temperature gradient, the derivation of an expression for thermal conductivity based on free electron movement in metals, and the Wiedemann-Franz law relating thermal conductivity to electrical conductivity.
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Engineering physics 4(Thermal conductivity)
- 1. 1 ENGINEERING PHYSICS Mr.Gouri Kumar Sahu Sr. Lecturer in Physics. 1 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. ENGINERING PHYSICSENGINERING PHYSICSENGINERING PHYSICSENGINERING PHYSICSENGINERING PHYSICSENGINERING PHYSICSENGINERING PHYSICSENGINERING PHYSICS Mr. Gouri Kumar Sahu Senior Lecturer in Physics C.U. T. M.
- 2. 2 ENGINEERING PHYSICS Mr.Gouri Kumar Sahu Sr. Lecturer in Physics. 2 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-5 5.1 Thermal conductivity The ratio of the amount of heat energy conducted per unit area of cross section per second to the temperature gradient. Therefore, the thermal conductivity ܭ ൌ െ ܳ ݀ܶ ݀ݔൗ ሾ4.1ሿ Where K =coefficient of thermal conductivity, Q=amount of heat energy conducted per unit area of cross section in one second ௗ் ௗ௫⁄ =temperature gradient. The negative sign shows that heat flows from the hot end to cold end. ܭ௧௧ ൌ ܭ௧ ܭ௦ ݁ݎ݄݁ݓ ݏ݄݊݊ ܽ݁ݎ ݄݁ݐ ݁݊݁ݕ݃ݎ ܿܽݏݎ݁݅ݎݎ ݂ݎ ݈ܽ݁ܿ݅ݐݐ ݏ݊݅ݐܽݎܾ݅ݒ
- 3. 3 ENGINEERING PHYSICS Mr.Gouri Kumar Sahu Sr. Lecturer in Physics. 3 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-5 5.2 Expression for thermal conductivity Let us consider a copper rod of appreciable length with unit area of cross- section in the steady state as shown in the figure. Let λ = AB = BC be the mean free path of the electron. The excess of energy carried by an electron from A to B = Hence the excess of energy transported by the process of conduction through unit area in unit time at the middle layer B = Similarly the deficit of energy transported through B in the opposite direction is
- 4. 4 ENGINEERING PHYSICS Mr.Gouri Kumar Sahu Sr. Lecturer in Physics. 4 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-5 5.2 Expression for thermal conductivity Let us assumes the number of free electrons flowing in a given direction through unit area in unit time is ଵ ݊ܿ̅. Thus the net energy transported through unit area in unit time from A to B is: ݊ܿ̅ߣ 6 ݀ܧ ݀ݔ െ െ ݊ܿ̅ߣ 6 ݀ܧ ݀ݔ ൌ ݊ܿ̅ߣ 3 ݀ܧ ݀ܶ ݀ܶ ݀ݔ The general expression for the quantity of heat energy transported through unit area for unit time is ܭ ௗ் ௗ௫ . Equating the two equations, one gets ݇ ൌ ݊ܿ̅ߣ 3 ݀ܧ ݀ܶ
- 5. 5 ENGINEERING PHYSICS Mr.Gouri Kumar Sahu Sr. Lecturer in Physics. 5 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-5 5.2 Expression for thermal conductivity But ௗா ௗ் is the energy required raising the temperature by one degree and hence it is ܥ௩ . Now ݇ ൌ ݊ܿ̅ߣ 3 ܥ௩ ൌ ݊ߣ 3 ܥ௩ 3݇ܶ ݉ But ܥ௩ ൌ ଷ ଶ ݇ with n=1 electron Thus, ݇ ൌ ఒ ଷ ଷ ଶ ݇ ଷಳ் ൌ ఒಳ ଶ ଷಳ்
- 6. 6 ENGINEERING PHYSICS Mr.Gouri Kumar Sahu Sr. Lecturer in Physics. 6 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-5 5.4 Wiedmann-Franz law This law states that when the temperature is not too law, the ratio of the thermal conductivity to the electrical conductivity of a metal is directly proportional to the absolute temperature, i.e., ఙ ∝ ܶ Or, ܭ ߪܶ ൌ ܿݐ݊ܽݐݏ݊ ൌ ܮ ሾ4.3ሿ Where L is a constant known as Lorentz number. From the expression for the thermal conductivity and electrical conductivity, the ratio can be written as, ܭ ߪ ൌ ݊ߣ݇ 2 3݇ܶ ݉ ൈ 12݉݇ܶ ݊݁ଶߣ ൌ 3 ݇ ݁ ଶ ܶ ሾ4.4ሿ Or, ఙ் ൌ 3 ಳ ଶ which is the Lorentz number.
- 7. 7 ENGINEERING PHYSICS Mr.Gouri Kumar Sahu Sr. Lecturer in Physics. 7 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. END OF SESSION -5 SESSION-5 THANK YOU