Explanation Given: Pressure to applied is P = 200 atm . Water must be compressed up to 99 % . Formula used: Expression for work done on the system is W = − ∫ v i v f P d V ...... (1) Here P is pressure, V i and V f are initial volume and final volume. Calculation: At a pressure of 200 atm, the volume of the water is reduced to 99 % of its value at atmospheric pressure 1 atm. Assume that the reduction in volume is linearly proportional to the increase in pressure. The pressure is calculated as P = A V + B ...... (2) Here A and B are constant, P is pressure and V is volume. At P = 1 atm , the volume is V = V o . And at P = 200 atm , the volume is V = 99 V o 100 . Let’s take the standard temperature and pressure, P = 1 atm , equation (2) can be written as by substitute V o for V 1 = A V o + B ...... (3) For P = 200 atm , equation (2) can be written as by substitute 99 V o 100 for V 200 = A 99 V o 100 + B ...... (4) Solve equation (3) and (4) for the value of A and B A = − 19900 V o atm. m -3 B = 19901 atm . Now equation (1) can be written as P = − 19900 V o V + 19901 ...... (5) Work required to compress 1 liter of water to 99% can be found by W = − ∫ 10 − 3 0.99 × 10 − 3 P d V ...... (6) Substitute 1 liter for W = − ∫ 10 − 3 0.99 × 10 − 3 ( − 2.016 × 10 12 V + 2.016 × 10 9 ) d V W = [ ( − 2.016 × 10 12 ) V 2 2 + ( 2.016 × 10 9 ) V ] 10 − 3 0.99 × 10 − 3 to solve A and B A = − 19900 1 × 10 − 3 . 101325 Pa 1 atm atm .m -3 A = − 2

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ISBN: 9780201380279

Author: Daniel V. Schroeder

Publisher: Addison Wesley

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Chapter 1.5, Problem 32P

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To Find:The work required to compress a liter of water.

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The given process. To Find: The work required to compress a liter of water.

Solution Summary: The author describes the process of compressing a liter of water.

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To Sketch: The given process.

To Find:The work required to compress a liter of water.

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Chapter 1 Solutions

The given process. To Find: The work required to compress a liter of water.

Solution Summary: The author describes the process of compressing a liter of water.

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To Sketch: The given process. To Find:The work required to compress a liter of water.

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Chapter 1 Solutions

To Sketch: The given process.

To Find:The work required to compress a liter of water.