# Net tension force net air pressure force figure 414

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net tension force net air pressure force Figure 4.14: Free body diagram for a sector of the spherical balloon surface. exerts a net upwards force on the balloon surface. The lateral pressure forces cancel each other. The net upwards force on this sector is balanced by a net downwards force exerted by the surface tension force of the balloon material. CC BY-NC-ND. 2011, J. M. Powers.

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96 CHAPTER 4. WORK AND HEAT Let us calculate the work: 1 W 2 = integraldisplay 2 1 PdV, (4.98) = k parenleftbigg 6 π parenrightbigg 1 / 3 integraldisplay V 2 V 1 V 1 / 3 dV, (4.99) = k parenleftbigg 6 π parenrightbigg 1 / 3 parenleftbigg 3 4 parenrightbigg bracketleftBig V 4 / 3 bracketrightBig V 2 V 1 , (4.100) = k parenleftbigg 6 π parenrightbigg 1 / 3 parenleftbigg 3 4 parenrightbigg parenleftBig V 4 / 3 2 V 4 / 3 1 parenrightBig , (4.101) = k parenleftbigg 6 π parenrightbigg 1 / 3 parenleftbigg 3 4 parenrightbigg V 4 / 3 1 parenleftBigg parenleftbigg V 2 V 1 parenrightbigg 4 / 3 1 parenrightBigg . (4.102) Now we know state 1, so this lets us determine k : k = P 1 parenleftbigg 6 V 1 π parenrightbigg 1 / 3 (4.103) Thus, the work is 1 W 2 = P 1 parenleftbigg 6 V 1 π parenrightbigg 1 / 3 parenleftbigg 6 π parenrightbigg 1 / 3 parenleftbigg 3 4 parenrightbigg V 4 / 3 1 parenleftBigg parenleftbigg V 2 V 1 parenrightbigg 4 / 3 1 parenrightBigg , (4.104) = P 1 V 1 parenleftbigg 3 4 parenrightbigg parenleftBigg parenleftbigg V 2 V 1 parenrightbigg 4 / 3 1 parenrightBigg , (4.105) = P 1 parenleftBigg 4 3 π parenleftbigg D 1 2 parenrightbigg 3 parenrightBigg parenleftbigg 3 4 parenrightbigg parenleftBigg parenleftbigg D 3 2 D 3 1 parenrightbigg 4 / 3 1 parenrightBigg , (4.106) = P 1 π parenleftbigg D 1 2 parenrightbigg 3 parenleftBigg parenleftbigg D 2 D 1 parenrightbigg 4 1 parenrightBigg , (4.107) = (150 kPa ) π parenleftbigg 0 . 4 m 2 parenrightbigg 3 parenleftBigg parenleftbigg 0 . 4 m 0 . 3 m parenrightbigg 4 1 parenrightBigg , (4.108) = 3 . 43612 kJ. (4.109) 4.3 Heat Let us make the following definition: Heat : a form of energy transferred across the boundary of a system at a given tem- perature to another system (or the surroundings) at a different temperature by virtue of the temperature difference between the two. CC BY-NC-ND. 2011, J. M. Powers.
4.3. HEAT 97 We adopt the notion that bodies do not contain heat, but that heat only has relevance as a type of energy that crosses system boundaries. Note that work is in a similar class; it is not contained within a system, but can be identified when it crosses system boundaries. We will make a distinction between heat and work energy transfers. We also note that when two bodies are at the same temperature, there can be no heat transferred between the two bodies. The subject of heat transfer considers the details of the heat transfer process. There are three fundamental classes of heat transfer: heat diffusion, also called conduction . Physically this is due to local effects. Bacon is fried via conduction effects as a culinary example. This is characterized by Fourier’s law 1 q = k T, (4.110) where q is the heat flux vector with units J/s/m 2 = W/m 2 , k is the thermal conduc- tivity with units

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