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Chapter 7: Problem 923

The compressibility of water \(4 \times 10^{-5}\) per unit atmospheric pressure. The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere will be.......... (A) \(4 \times 10^{-5} \mathrm{CC}\) (B) \(4 \times 10^{-5} \mathrm{CC}\) (C) \(0.025 \mathrm{CC}\) (D) \(0.004 \mathrm{CC}\)

Short Answer

Expert verified
The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere is \(0.4 \, \mathrm{CC}\). The given options appear to be incorrect, as none of them match the calculated answer.

Step by step solution

01

Identify the variables

We have the following information given: - Compressibility of water = \(4 \times 10^{-5}\) per unit atmospheric pressure - Volume of water = 100 cubic centimeters (CC) - Applied pressure = 100 atmospheres (atm)
02

Use the formula for finding the decrease in volume

The formula for finding the decrease in volume using compressibility, volume, and applied pressure is: Decrease in Volume = Compressibility × Volume × Applied Pressure
03

Substitute the given values into the formula

Substitute the given values into the formula: Decrease in Volume = \((4 \times 10^{-5})(100)(100)\)
04

Calculate the decrease in volume

Now, we can calculate the decrease in volume: Decrease in Volume = \((4 \times 10^{-5})(100)(100) = 0.4\, \mathrm{CC}\)
05

Choose the correct answer from the options

Comparing the calculated decrease in volume with the given options, we can conclude that the correct answer is: (A) \(4\times10^{-5}\,\mathrm{CC}\) (Incorrect) (B) \(4\times10^{-5}\,\mathrm{CC}\) (Incorrect) (C) \(0.025\,\mathrm{CC}\) (Incorrect) (D) \(0.004\,\mathrm{CC}\) (Incorrect) However, the calculated decrease in volume is not among the given options. The closest option is \(0.004\,\mathrm{CC}\), but the correct answer should be \(0.4\,\mathrm{CC}\). There seems to be an error in the given answer choices.

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