Question

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? The bulk modulus of ice is 2.0 × 109 N/m2, and 1 ATM = 1.01 × 105 N/m2.

Answer 1

Answer:

The pressure increase inside the automobile engine block is 1782.18 ATM

Explanation:

Given;

the change in volume of water, ΔV = 9%

the bulk modulus of ice, K = 2 x 10⁹ N/m²

Bulk modulus is given by;

$K = -V\frac{dP}{dV}$

for pressure increase in the automobile engine block, when the water in there froze;

$dP = K(\frac{dV}{V} )\\\\dP = K(\frac{0.09V}{V} )\\\\dP = 0.09K\\\\dP = 0.09 (2*10^9)\\\\dP = 1.8 *10^{8} \ N/m^2\\\\dP = 1782.18 \ ATM$

Therefore,  the pressure increase inside the automobile engine block is 1782.18 ATM