17.2 Work Done by an Expanding Gas

17.2 Work Done by an Expanding Gas - Work Done by an...

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Work Done by an Expanding Gas Learning Goal: To derive the expression for the work done by an expanding gas, , and to understand how it follows from the expression for mechanical work. Especially from the historically important perspective of making engines to convert heat energy into work, the work in thermodynamics is defined as the work done by the system on the exterior world, and not vice versa as is done in the rest of classical mechanics. In classical mechanics, one always considers the work done on a system by the outside world. Rarely does one think about the work done by the system. Suppose you push a large block with a certain force of magnitude over some distance. You have done work on the block; hence the energy of the block should increase. According to Newton's 3rd law, the block exerts the same magnitude of force , but in the opposite direction (i.e., directed back at you). Hence, the work done by the block (on you) is negative, since the direction of motion opposes the direction of the force. In summary, you have to be careful about the sign of the work: the same situation gives opposite signs of the work depending on whether our perspective is classical mechanics or thermodynamics. In thermodynamics, one often deals with liquids and gases that exert forces on their containers (i.e., the fluids exert pressure over an area). If the container changes volume, then this force acts through a distance and hence does work. For a steam engine, the example pictured here, the "container" is a cylinder whose volume changes as the piston slides in or out. Suppose a gas is confined within the cylinder. The pressure of the gas is , and the area of the cylinder is . Consider the work done as the gas expands, pushing the piston to the right. Call the infinitesimal distance the piston moves . A. What force does the gas exert on the piston? (Note that the positive x axis is to the right in the figure.) Express the force in terms of , , and any constants, = p*A B. If the piston moves a distance , what is , the work done by the gas? Express the work done by the gas in terms of given quantities. = p*A*dx C. What is , the increase in volume of the gas? Express the differential increase in terms of and other given quantities. = A*dx D. Now find the work done by the gas in terms of the thermodynamic variables.
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Express the differential work in terms of thermodynamic variables such as the gas's pressure , temperature , volume , and its change in volume . = p*dV E. Suppose that the gas expands from to at constant pressure . How much work is done by the gas? Express the work in terms of , , and . = p_0*(V_1-V_0) F. Is the work you just computed positive or negative? positive
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This note was uploaded on 09/09/2011 for the course PHYSICS 142 taught by Professor Hoffman during the Spring '09 term at Ill. Chicago.

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17.2 Work Done by an Expanding Gas - Work Done by an...

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