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 :

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 : (A) (P/3 α K) (B) (P/ α K) (C) (3 α/P K) (D) 3 P K α

Tardigrade Admin · Accepted Answer

K = (Δ P/(-(Δ V )V)) (Δ V/V) = (P/K) ∴ V = V0 (1 + &gamma;Δ t ) (Δ V/V0) = &gamma;Δ t ∴ (P/K) = &gamma;Δ t ⇒ Δ t = (P/&gamma; K ) =(P/3 α K)

$\frac{P}{3 α K}$

$\frac{P}{α K}$

$\frac{3 α}{P K}$

$3 P K α$

$K = \frac{Δ P}{( - \frac{Δ V}{V} )}$
$\frac{Δ V}{V} = \frac{P}{K}$
$∴ V = V_{0} (1 + γ Δ t)$
$\frac{Δ V}{V _{0}} = γ Δ t$
$∴ \frac{P}{K} = γ Δ t$
$\Rightarrow Δ t = \frac{P}{γ K} = \frac{P}{3 α K}$

3αKP​

αKP​

PK3α​

3PKα

K=(−VΔV​)ΔP​ VΔV​=KP​ ∴V=V0​(1+γΔt) V0​ΔV​=γΔt ∴KP​=γΔt ⇒Δt=γKP​=3αKP​

$\frac{P}{3 α K}$

$\frac{P}{α K}$

$\frac{3 α}{P K}$

$3 P K α$

$K = \frac{Δ P}{( - \frac{Δ V}{V} )}$
$\frac{Δ V}{V} = \frac{P}{K}$
$∴ V = V_{0} (1 + γ Δ t)$
$\frac{Δ V}{V _{0}} = γ Δ t$
$∴ \frac{P}{K} = γ Δ t$
$\Rightarrow Δ t = \frac{P}{γ K} = \frac{P}{3 α K}$