Question

A piece of aluminum (bulk modulus 7.1 x 1010 N/m2) is placed in a vacuum chamber where the air pressure is 0.781 x 105 Pa. The vacuum pump is then turned on and the pressure is further reduced to zero. Determine the fractional change V/V0 in the volume of the aluminum

Answer 1

Answer:

${\dfrac{\Delta V}{V}}=11\times 10^{-7}$

Explanation:

Given that

Bulk modulus ,K = 7.1 x 10¹⁰  Pa

The pressure P₁ = 0.781 x 10⁵ Pa

The final pressure P ₂ = 0 Pa

We know that bulk modulus given as

$K=\dfrac{\Delta P}{\dfrac{\Delta V}{V}}$

Now by putting the values

$K=\dfrac{\Delta P}{\dfrac{\Delta V}{V}}$

$7.1\times 10^{10}=\dfrac{0.781\times 10^5}{\dfrac{\Delta V}{V}}$

${\dfrac{\Delta V}{V}}=\dfrac{0.781\times 10^5}{7.1\times 10^{10}}$

${\dfrac{\Delta V}{V}}=11\times 10^{-7}$

Therefore fractional change will be 11 x 10⁻⁷.