Water at 1 atm pressure is compressed to 430 atm pressure isothermally. Determine the increase in the density of water. Take the isothermal compressibility of water to be 4.80 * 10-5 atm-1. The density of water at 20°C and 1 atm pressure is rho1 = 998 kg/m3.

compressibility = 1 / bulk modulus of elasticity (B)

B = 1 / 4.8 x 10⁻⁵ = Δp / Δv / v (Δp is change in pressure, Δv is change in volume)

1 / 4.8 x 10⁻⁵ = 429 / Δv / v

Δv / v = 429 x 4.8 x 10⁻⁵

= 2059.2 x 10⁻⁵

=.021

v = m / d (d is density and m is mass of the water taken)

taking log and then differentiating

Δv / v = - Δd / d

-.021 = - Δd / d

Δd =.021 x d

=.021 x 998

= 20.9

new density

= 998 + 20.9

1018.9 kg/m3