Thermal Properties of Matter

JEE Main level, single correct, medium

42 of 126

Question 42 of 126

An external pressure PP is applied on a cube at 0∘C0^{\circ}C so that it is equally compressed from all sides. KK is the bulk modulus of the material of the cube and α\alpha 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:

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Answer: (B) P3αK\dfrac{P}{3\alpha K}

B=−P(dVV)B=\dfrac{-P}{\left(\dfrac{dV}{V}\right)}

dVV=−PB\dfrac{dV}{V}=\dfrac{-P}{B}

dV=−PVBdV=\dfrac{-PV}{B}

ΔV=VγΔTΔVV=γΔT\Delta V=V\gamma \Delta T\dfrac{\Delta V}{V}=\gamma \Delta T

ΔVV=3αΔT\dfrac{\Delta V}{V}=3\alpha \Delta T

K=PΔVV=P3αΔTK=\dfrac{P}{\dfrac{\Delta V}{V}}=\dfrac{P}{3\alpha \Delta T}

ΔT=P3αk\Delta T=\dfrac{P}{3\alpha k}

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