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Chapter 25: Problem 2800

The compressibility of a substance equals......... (A) \((\Delta \mathrm{V} / \mathrm{PV})\) (B) \(\\{(\mathrm{P} \Delta \mathrm{V}) / \mathrm{V}\\}\) (C) \(\\{\mathrm{V} /(\mathrm{P} \Delta \mathrm{V})\\}\) (D) \((\mathrm{PV} / \Delta \mathrm{V})\)

Short Answer

Expert verified
None of the given options are correct. The correct formula for compressibility is: \(compressibility = \frac{-1}{V} \cdot \frac{\Delta V}{\Delta P}\).

Step by step solution

01

Option A: Check if the given formula represents compressibility.

The formula in this option is: (A) \((\Delta \mathrm{V} / \mathrm{PV})\) However, this formula does not represent compressibility, since it represents the change in volume divided by the product of initial pressure and volume. The correct formula for compressibility should have the pressure change in the numerator.
02

Option B: Check if the given formula represents compressibility.

The formula in this option is: (B) \(\\{(\mathrm{P} \Delta \mathrm{V}) / \mathrm{V}\\}\) This formula also doesn't represent compressibility, as it has the product of the initial pressure and the change in volume divided by the initial volume. The correct formula for compressibility should have the pressure change in the numerator.
03

Option C: Check if the given formula represents compressibility.

The formula in this option is: (C) \(\\{\mathrm{V} /(\mathrm{P} \Delta \mathrm{V})\\}\) Once again, this formula doesn't represent compressibility, as it has the initial volume divided by the product of the initial pressure and the change in volume. The correct formula for compressibility should have the pressure change in the numerator.
04

Option D: Check if the given formula represents compressibility.

The formula in this option is: (D) \((\mathrm{PV} / \Delta \mathrm{V})\) Again, this formula doesn't represent compressibility, as it has the product of the initial pressure and the initial volume divided by the change in volume. The correct formula for compressibility should have the pressure change in the numerator. In conclusion, none of the given options represent the correct formula for compressibility. The correct formula for compressibility is: \(compressibility = \frac{-1}{V} \cdot \frac{\Delta V}{\Delta P}\)

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Most popular questions from this chapter

Arrange rubber, steel and glass in the order of decreasing elasticity. (A) glass, steel, rubber (B) rubber, glass, steel (C) glass, rubber, steel (D) steel, glass, rubber

Two rods of different materials having coefficients of thermal expansions \(\alpha_{1}, \alpha_{2}\) and Young's module \(\mathrm{y}_{1}, \mathrm{y}_{2}\) respectively are fixed between two rigid walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rod. if \(\alpha_{1}: \alpha_{2}=2: 3\) the thermal stresses developed in the rod are equal provided \(\mathrm{y}_{1}: \mathrm{y}_{2}\) equals. (A) \(3: 2\) (B) \(2: 3\) (C) \(4: 9\) (D) \(1: 1\)

A solid sphere of radius \(\mathrm{R}\) made of a material of bulk modulus \(\mathrm{K}\) is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass \(\mathrm{M}\) is placed on the pisten to compress the liquid, the fractional change in the radius of the sphere \((\delta \mathrm{R} / \mathrm{R})\) is.......... (A) \(\\{(\mathrm{Mg}) /(3 \mathrm{KA})\\}\) (B) \(\\{(\mathrm{Mg}) /(\mathrm{KA})\\}\) (C) \(\\{(\mathrm{Mg}) /(4 \mathrm{KA})\\}\) (D) \(\\{(\mathrm{Mg}) /(2 \mathrm{KA})\\}\)

In searle's experiment, diameter of wire was measured \(0.05\) \(\mathrm{cm}\) by screw gauge of least count \(0.001 \mathrm{~cm}\). The length of wire was measured \(110 \mathrm{~cm}\) by metes scale of least count \(0.1 \mathrm{~cm}\). When a weight of \(50 \mathrm{~N}\) is suspended from the wire, extension is measured to be \(0.125 \mathrm{~cm}\) by a micrometer of lecst count $0.001 \mathrm{~cm} .$ Find maximum error in the measurement of Young's modulus of the wire material. (A) \(1.09 \times 10^{12}\) (B) \(1.09 \times 10^{10}\) (C) \(3.09 \times 10^{10}\) (D) \(3.09 \times 10^{12}\)

A solid cylindrical steel column is \(4 \mathrm{~m}\) long and \(9 \mathrm{~cm}\) in diameter $\cdot\left(\mathrm{Y}_{\text {steel }}=1.9 \times 10^{11} \mathrm{Nm}^{-2}\right)$. The decrease in length of the column, while carrying a load of \(80000 \mathrm{~kg}\) is........ (A) \(3.2 \mathrm{~mm}\) (B) \(1.8 \mathrm{~mm}\) (C) \(4.4 \mathrm{~mm}\) (D) \(2.6 \mathrm{~mm}\)
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