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Question:

An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

3PKα

3αPK

P3αK

PαK

Solution:

K=PΔV/V₀ (by definition) (1)
also, Vf=V₀(1+rΔT) Where r=3α_(2)
ΔV=Vf−V₀ ⇒ΔV=Vf−V₀=V₀rΔT
Putting in (1)
K=PV₀rΔT/V₀=PrΔT
⇒ΔT=K/Pr=P/3Kα using (2)