Solids Elasticity (Bulk Modulus)

[asoz]

Homework Statement

When the water freezes it expands by about 9.00%. What pressure increase would occur inside your automobile engine block if the water in it froze?(The bulk modulus of ice is 2.00 x 10^9 N/m^2).

Homework Equations

B=\frac{\Delta P}{\Delta V / V_i}

The Attempt at a Solution

If I solve the problem "forward in time" I get this:
\Delta P=\frac{1.09V_i-Vi}{Vi}B=0.09B

but if solving the problem "backwards in time"

\Delta P = \frac{V_i-1.09V_i}{1.09V_i}B = 0.0826B

Shouldn't both answers have the same magnitude?

 

[Mapes]

No; 90% of 110% of x is not x, for example.

 

[asoz]

Of Course. Thanks