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Question: A glass slab is subjected to a pressure of 10 atm. The fractional change in its volume is (Bulk mod...

A glass slab is subjected to a pressure of 10 atm. The fractional change in its volume is

(Bulk modulus of glass=37 × 109 N m−2,= 37\ \times \text{ 1}\text{0}^{9}\text{ N }\text{m}^{- 2}, and

1 atm =1 × 105 N m−2)1\text{ atm } = \text{1 } \times \text{ 1}\text{0}^{5}\text{ N }\text{m}^{- 2})

A

2.7 × 10−22.7\ \times \text{ 1}\text{0}^{- 2}

B

2.7 × 10−32.7\ \times \text{ 1}\text{0}^{- 3}

C

2.7 × 10−42.7\ \times \text{ 1}\text{0}^{- 4}

D

2.7 × 10−52.7\ \times \text{ 1}\text{0}^{- 5}

Answer

2.7 × 10−52.7\ \times \text{ 1}\text{0}^{- 5}

Explanation

Solution

: Bulk modulus, B=PΔV/VB = \frac{P}{\Delta V/V}

∴\thereforeFractional change in volume, ΔVV=PB\frac{\Delta V}{V} = \frac{P}{B}

Here, P=10atm=10×1×105Nm−2P = 10atm = 10 \times 1 \times 10^{5}Nm^{- 2}

B=37×109Nm−2B = 37 \times 10^{9}Nm^{- 2}

∴ΔVV=1×106Nm−237×109Nm−2=0.027×10−3=2.7×10−5\therefore\frac{\Delta V}{V} = \frac{1 \times 10^{6}Nm^{- 2}}{37 \times 10^{9}Nm^{- 2}} = 0.027 \times 10^{- 3} = 2.7 \times 10^{- 5}