First slide

Thermal expansion

Question

A uniform pressure P is exerted on all sides of a solid cube at $t^{o} c$ , by what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? (K is bulk modulus and $α$ is coefficient of linear expansion?

Moderate

A

$\frac{K}{3Pα}$
B

$\frac{P}{3Kα}$
C

$\frac{α}{3KP}$
D

$\frac{3}{KP}$

Solution

$b u l k m o d u l l u s o f a m a t e r i a l i s K= \frac{P}{\frac{ΔV}{V}}; here P is pressure, ΔV is change in volume, V is initial volume \frac{ΔV}{V} = \frac{P}{K} .........(1) c o e f f i c i e n t o f l i n e a r e x p a n s i o n i s α= \frac{Δl}{l.ΔT}; here Δ l c h a n g e i n l e n g t h; l i s i n i t i a l l e n g t h; ΔT i s c h a n g e i n t e m p e r a t u r e c o e f f i c i e n t o f v o l u m e e x p a n s i o n i s γ = 3 α \frac{ΔV}{V ΔT} = 3. α \frac{ΔV}{V} = 3. α.ΔT s u b s t i t u t e e q n (1) \frac{P}{K} = 3. α.ΔT ΔT = \frac{P}{3Kα}$

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