Heat Transfer PDF

Okay, here is the text from the images converted to markdown format. ### Thermal Expansion When matter is heated, the kinetic energy of its constituent molecules increases, resulting in expansion. This is called thermal expansion, as shown in fig. 6.3. Let us understand thermal expansion in matter...

Okay, here is the text from the images converted to markdown format. ### Thermal Expansion When matter is heated, the kinetic energy of its constituent molecules increases, resulting in expansion. This is called thermal expansion, as shown in fig. 6.3. Let us understand thermal expansion in matter in different states. ### Thermal expansion in solids As we know, solids have a definite shape and volume. If heat is given to a solid, there can be a change in its length, area, or volume. That is why when a metal lid is heated when jammed over a bottle, it opens up. Let us discuss different kinds of expansion in solids. ### Linear expansion When a metal rod is heated, its length increases. This phenomenon is called **linear expansion**, depends upon the following factors: 1. **The original length of the solid:** Linear expansion is directly proportional to the length of the solid. That is why solids with different lengths if given the same heat, the longer solid will expand more than the shorter one. 2. **Increase in temperature:** Linear expansion in solids varies directly with the increase in temperature. 3. **Nature of material of the solid:** Different materials have different temperature toleranceSo, there will be different linear expansions for different solids even if they are heated for the same temperature change. The criteria that justify the material aspect of the solid is called the **coefficient of linear expansion**. For a rod of initial length $L_1$ if heated to a temperature increase of T and its length increases to $L_2$then, coefficient of linear expansion is given by $\alpha = \frac{(L_2 - L_1)}{L_1T}$ $\alpha$ is called the **coefficient of linear expansion** It is the ratio of the change in length of a heated solid to the change in temperature for the original length. It is different for different materials. Its SI unit is per °C. ### Superficial expansion When a solid is heated, there is a change in its surface area as its dimensions increase along both length and breadth. This is called **superficial expansion**. Very much like linear expansion, superficial expansion of solids depends upon the following factors: 1. **Increase in temperature:** The more the heat provided, the more will be rise in temperature and hence more superficial expansion. 2. **The original area of the solid:** A solid with a larger area undergoes more superficial expansion as compared to one with less area if the same amount of heat is provided. 3. **Nature of material of the solid:** Different materials expand differently. For example, an iron plate expands more compared to a copper plate if the same heat is provided. **Coefficient of superficial expansion:** The material property of any solid to undergo superficial expansion is considered in terms of the coefficient of superficial expansion. It is the ratio of the change in surface area of a heated solid to the change in temperature for the original surface area. The change in the area of an object is directly related temperature for the orignal surface area. For a metal sheet of initial area $A_1$, if heated to a temperature increase of T and its area increases to $A_2$, then, $\beta = \frac{(A_2 - A_1)}{A_1T}$ $\beta$ is called the coefficient of superficial expansion. Its Sl unit is per °C. ### ACTIVITY Take a thin metal sheet and make a small hole in it such that a nail cannot pass through it. Now heat the metal sheet near to the hole in the sheet, using a burner for sufficient time. Again try to pass the nail through the hole. This time the nail will pass through the hole. Why has it happened? On heating the metal sheet, it expanded. Because of the stretch, the size of the hole also increased. And hence nails could now easily pass through the hole. It confirms the superficial expansion. ### Cubical Expansion The corresponding change in the volume of a solid, when it is heated, is called **cubical expansion**. It is also known as volume expansion. The cubical expansion of a solid depends on the following factors: 1. **Increase in temperature:** The more the amount of heat provided to a solid, the greater will be its cubical expansion. 2. **Original volume of the solid:** The greater the original volume, the more will be the cubical expansion. 3. **Nature of material of the solid:** Cubical expansion also depends upon the nature of the solid material. The coefficient of cubical expansion justifies the material nature of the cubical expansion. For a solid object of initial volume $V_1$ if heated to a temperature increase of T and its volume increases to $V_2$ then, $Y = \frac{(V_2 - V_1)}{V_1T}$ Y is called the coefficient of cubical expansion. It is the ratio of the change in volume of a heated solid to the change in temperature for the original volume Its Sl unit is per °C. The values of coefficient of linear expansion of different solids is given in Table 6.1. Table 6.1. Thermal coefficients of some solids (per °C) | Solids | Linear expansion (°C) | | ----------- | ----------- | | Aluminium | 23 x $10^{-6}$ | | Brass | 19 x $10^{-6}$ | | Copper | 17 x $10^{-6}$ | | Glass | 8.5 x $10^{-6}$ | | Iron | 12 x $10^{-6}$ | For a solid undergoing thermal expansion, all the coefficients of thermal expansions are related to each other by the equation, $\alpha = 2\beta = 3\gamma$. ### Thermal expansion in liquids The kinetic theory of matter can explain the expansion of solids because of heating. The molecules of a liquid are much free compared to a solid. Liquids do not have a fixed shape, but they do have a fixed volume, That is why liquids undergo only cubical expansion when heated. 1. **Original volume of a liquid:** The greater the volume of a liquid, the more will be its cubical expansion. 2. **Change in temperature:** The more the amount of heat provided to a liquid, the greater will be its cubical expansion. 3. **Nature of the liquid:** Different liquids expand differently for the same volume considered and the same heat provided. That is why the nature of expansion in mercury is different from water or any other liquid, even when the same heat is provided. ### Thermal expansion in gases The property of gases is very different from solids and liquids because they neither have a fixed shape nor a fixed volume. Expansion in the case of gases is understood by the expansion they can cause in the container in which they are kept. ### Experiment 6.1 Aim: To show that gases show thermal expansion Materials required: Empty metal bottle, rubber balloon, water bath, tripod stand, burner and water. Procedure: 1. Take an empty metal bottle with a narrow neck opening. Tie a balloon on its neck. 2. Place the metal bottle now in a water bath having water and start boiling the same. Observation: On heating, the balloon gets inflated. It happened because air inside the bottle expanded and pushed the balloon walls outward. Conclusion: Gases expand on heating. ### Comparison of thermal expansions in three states of matter All three states of matter have different expansions to the heat provided. Comparison of thermal expansions in different states of matter given in Table 6.2. Table 6.2. Comparison of thermal expansion between different states of matter | Solids | Liquids | Gases | | --------------------------------------------------------- | ---------------------------------------------------- | ---------------------------------------- | | Solids show linear, superficial, and cubical expansion. | Liquids show only cubical expansion. | Gases show only cubical expansion. | | The degree of expansion is the least. | The degree of expansion is more than solid. | The degree of expansion is most. | ### Applications of Thermal Expansions in Daily Life There are various applications of thermal expansion in our daily life. Let us discuss some of them. #### In solids 1. A considerable amount of gap is left between the two sections of a railway track as shown in fig. 6.4. It is done to cope with the expansion of iron especially during summer. Because of heat, it is possible that iron will expand, which can lead to deformity in railway tracks. This can lead to the derailment of trains. 2. The iron rim fitted to the wooden wheel is slightly lesser in diameter than the wooden wheel. It is specifically designed by first heating the iron rim so as to expand initially. Then it is kept on the wooden wheel to cool down. It contracts with cooling and fits firmly on the wooden wheel 3. When hot tea or milk is poured into a glass, it cracks. It happens because glass is a poor conductor of heat.The imbalance in the expansion of the glass leads to its cracking. #### In liquids 1. The application of mercury in the capillary of a thermometer is based on its property of cubical expansion. When the bulb of a thermometer comes into contact with a hot object, the heat gets transferred to the mercury. Then mercury expands itself and rises inside the tube. The expansion of mercury is more uniform and does not stick to the tube. It makes mercury an ideal thermometric fluid. 2. In many medicine bottles, a marginal gap is left between the seal and cap of bottle to cope with the potential expansion that can happen if the medicines are to be kept in warm or summer conditions #### In Gases 1. Gas thermometers are based on the property of cubical expansion of gases. 2. During summer, it is advised not to inflate the tyres of vehicles completely. The marginal space is left so that the expanding gas can accommodate itself without bursting the tyres. ### Quick Check Write T for true and F for false. 1. All matters expand equally when heated. **F** 2. Railway tracks are laid with some gap between their sections. **T** 3. Gas thermometers have mercury in them. **F** 4. Solids only show cubical expansion. **F** 5. Coefficient of thermal expansions are material specific. **T**