Question

A block of metal whose volume
expansivity is 5.0 × 10−5 °C−1 and
isothermal compressibility is 1.2 ×
10−6 atm−1 has volume 5 litre at 1
atm and 20 °C. On applying
pressure, its temperature rises by
12°C and volume increases by 0.5
cm3. Calculate the pressure applied.

Answer 1

 Due to increase in pressure the volume decreases.  Due to increased temperature volume increases.  So the net increase is 0.5 cc given.

Expected expansion in volume due to ΔT = 12° C is 
  = 5000 cc * 5.0 * 10⁻⁵ /⁰C * 12°C = 3 cc
Actual increase = 0.5 cc
So compression in volume due to ΔP = 2.5 cc

Compressibility = - 1/V * ΔV / ΔP = β_T = 1.2 * 10⁻⁶ /atm
$-\frac{1}{V}\frac{\Delta V}{\Delta P}|_T=\beta_T$

ΔP = 2.5 / [ 5000 * 1.2 * 10⁻⁶) = 416.67 atm

Pressure applied = P + ΔP = 417.67 atm