Question

For acetic acid at 20 °C and 1 bar,

B = 1.08×10−3 /°C, κ = 9.08×10−5 /bar, V = 0.951 L/kg

a). Compute the change in volume and work done when one kilogram of the substanceis heated from 15°C to 25 °C at a constant pressure of 1 bar.

b). Compute the change in volume and work done when on kilogram of the substance is compressed from 1 bar to 100 bar at a constant temperature of 20°C.

Answer 1

We have

dV/V = βdT - κdP

a) At constant pressure, dV/V = βdT

Thus, ln(V2/V1) = β(T2 - T1)

Substituting values,

ln(V2/0.951) = (1.08 x 10^-3) x 10

V2 = 0.9613 L

Change in volume = 0.010326 L

B) Now, since dT=0

dV/V = -κdP

ln(V2/V1) = k(P1-P2)

Substituting values,

ln(V2/0.951) = 9.08 x 10^-5 x (-99)

V2 = 0.94249 L

Change in volume = -0.00851 L

Considering reversible conditions, this is isothermal work,

W=-nRTln(P1/P2)

n= 1000g/60 g/mol = 16.667 mol

W = - 16.6667 x 8.314 x 293 x ln(100) = -186.97 kJ