An external pressure $P$ is applied on a cube at $0^o C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and a 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
An external pressure $P$ is applied on a cube at $0^o C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and a 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
- [JEE MAIN 2017]
- A
$\frac{P}{{3\alpha K}}$
- B
$\;\frac{P}{{\alpha K}}$
- C
$\;\frac{{3\alpha }}{{PK}}$
- D
$\;3PK\alpha $
Similar Questions
Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the mid point of $PQ.$ Distance $OR$ remains same for small change in temperature. Coefficient of linear expansion for $PR$ and $RQ$ is same i.e. ${\alpha _2}$ but that for $PQ$ is ${\alpha _1}$. Then relation between ${\alpha _1}$ and ${\alpha _2}$ is
Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the mid point of $PQ.$ Distance $OR$ remains same for small change in temperature. Coefficient of linear expansion for $PR$ and $RQ$ is same i.e. ${\alpha _2}$ but that for $PQ$ is ${\alpha _1}$. Then relation between ${\alpha _1}$ and ${\alpha _2}$ is
Give value of coefficient of volume expansion at room temperature for ideal gas.
Give value of coefficient of volume expansion at room temperature for ideal gas.
A metallic bar of Young's modulus, $0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ and coefficient of linear thermal expansion $10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, length $1 \mathrm{~m}$ and area of cross-section $10^{-3} \mathrm{~m}^2$ is heated from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ without expansion or bending. The compressive force developed in it is :
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- [NEET 2024]
A blacksmith fixes iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are $5.243\; m$ and $5.231\; m$, respectively at $27^oC$. To what temperature (in $^oC$) should the ring be heated so as to fit the rim of the wheel?
A blacksmith fixes iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are $5.243\; m$ and $5.231\; m$, respectively at $27^oC$. To what temperature (in $^oC$) should the ring be heated so as to fit the rim of the wheel?
Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at $0^o C$ while the tube on the right is kept at $30^o C$ in a water bath. The difference in the levels of the liquid in the two tubes is $4 \,\,cm$ while the height of the liquid column at $0^o C$ is $120\,\,cm$. The coefficient of volume expansion of liquid is (Ignore expansion of glass tube)
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