A cylinder with a frictionless, movable piston like that shown in the figure, contains a quantity of helium gas. Initially the gas is at a pressure of 1.00×105Pa, has a temperature of 300K, and occupies a volume of 1.50L. The gas then undergoes two processes. In the first, the gas is heated and the piston is allowed to move to keep the temperature equal to 300K. This continues until the pressure reaches 2.50×104Pa. In the second process, the gas is compressed at constant pressure until it returns to its original volume of 1.50L. Assume that the gas may be treated as ideal. Find the volume, in liters, of the gas at the end of the first process

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Asked Nov 12, 2019
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A cylinder with a frictionless, movable piston like that shown in the figure, contains a quantity of helium gas. Initially the gas is at a pressure of 1.00×105Pa, has a temperature of 300K, and occupies a volume of 1.50L. The gas then undergoes two processes. In the first, the gas is heated and the piston is allowed to move to keep the temperature equal to 300K. This continues until the pressure reaches 2.50×104Pa. In the second process, the gas is compressed at constant pressure until it returns to its original volume of 1.50L. Assume that the gas may be treated as ideal. Find the volume, in liters, of the gas at the end of the first process

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Step 1

For the first part the temperature T is kept constant.

Hence, using Boyle’s law according to which,

 

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P,V

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Step 2

Here P1 and V1 are the initial pressure and volume of the gas and P2 and V2 are the final pressure and volume of the gas.

Substitute 1.00(105) Pa for P1, 1.50 L for V1 and 2.50(104)...

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(1.00(10 )Pa) (.50L)-(2.50(10 )Pa )V, (1.00(10) Pa) (1.50L) 2.50(10)Pa 6.0L

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