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A case of transformation of heat into work

 

When the piston moves in the opposite direction, steam enters the cylinder B and used steam is forced out at A. With this simple arrangement, the steam would leave the cylinder on exhaust at a temperature nearly as high as that at which it entered it. A considerable quantity of heat would thus be carried to the condenser or the outside air and lost so far as useful work is concerned. In order to prevent this waste as far as possible, an automatic cutoff is provided. When the piston has moved through about one fourth of its stroke, this slide valve automatically cuts off the supply of steam.

After this cutting off of the steam from the steam chest the steam that has already entered the cylinder expands and pushes the piston for­ward, through the remainder of the stroke. During this expansion, the piston is doing work, the pressure of the steam is being reduced, and the temperature of the steam is lowered. The heat contained in the steam is thus converted into useful work.

When the piston has reached the end of this stroke, the slide valve opens A and connects В to the steam chest. Live steam is now again admitted to the cylinder behind the piston and it pushes the piston toward the left. The dead steam in front of the piston is forced through A. When, as before, the piston has made about one fourth of its stroke, the slide valve closes B, and the steam behind the piston expands until the piston has reached the end of its stroke. The cycle is then repeated.

The pressure of the steam in the boiler is regulated by means of a pop valve, which allows the steam to escape when the pressure exceeds a certain value.

Gas Engine. - Gas engines and gasoline engines operate on the same principle. In each case the energy is derived from the explosion of a mixture of air and gas or gasoline vapor. The gasoline engine is now the commonest type of engine. It is used to drive motorcars, motorboats, tractors, etc.

Work Done by a Gas Expanding at Constant Pressure. -Let a volume of gas be enclosed behind a piston which is airtight and which moves without friction. Let the pressure acting on the piston be denoted by p and the area of the piston by S. The total force acting on the piston pushing it backward is



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F=pS

If, now, the gas in the cylinder is heated, it may be allowed to expand without any change in its pressure, and the piston moves back through a distance x. Work done on piston = force X distance = p X S X x

Now S X x = increase of volume of the gas during expansion.

Hence

Work = p X change in volume

It is convenient to represent the work done by the gas by plotting the pressure of the gas on the vertical axis and the volume of the gas on the horizontal axis. In this case, the pressure is constant for all volumes. Hence, AB represents the relation between the volume and the pressure. If V1 denotes the original volume and V2 the final vol­ume, the length of the line ab represents the change in volume during expansion. The product of the change in volume and the pressure is represented by the rectangle ABba. This area stands for the work done by the gas during its expansion; and since this work is equal to the heat supplied to the gas during expansion, this rectangle also repre­sents the heat taken in by the gas during its expansion.

Work Done by a Gas Expanding at Variable Pressure. -If the gas expands under a variable pressure, the work which it performs may be represented by a diagram similar to that represent­ing the work done by a gas expanding at constant pressure. In this case the line AB (Figure 35), instead of being horizontal as in the pre­ceding case, slopes toward the horizontal axis along which the volumes are plotted. Nevertheless, the area under AB will represent the work done by the gas as it expands with changing pressure. It is pos­sible to construct a rectangle having the same base as the figure ABba and the same area. The height of this rectangle would be the average pressure of the gas during its expansion. If the varying pressure acting on the piston has been replaced by a constant pressure equal to the average pressure, the work done by the gas will remain unchanged. The average pressure may then be defined as the constant pressure by which a varying pressure may be replaced without changing the amount of work done on the piston for the same stroke.

 

 

Figure 35 - Work done by a gas at va­riable pressure

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<== попередня сторінка | наступна сторінка ==>
 | Equals average pressure times change of volume

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