(1) P/3αβ
The decrease in volume due to volumetric strain of pressure P should be equal to increase in volume due to thermal expansion. We have
β = The Bulk modulus = p/volumetric strain = P/v/V = PV/v
∴ v = PV/β ----(1)
v is decrease in volume
The volume V' when temperature is raised to t°C = V + γ Vt = V + 3α Vt [∵ γ = 3α]
Increase in volume = v = V'–V = 3α Vt .....(2)
From (1) and (2) we have