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  • A constant pressure P is applied on all sides of a sphere at a certain temperature. By what amount should the temperature of the sphere by raised in order to bring its volume to the value it h

A constant pressure P is applied on all sides of a sphere at a certain temperature. By what amount should the temperature of the sphere by raised in order to bring its volume to the value it had before the pressure was applied? The coefficient of volume expansion of the material of the sphere is \mathrm{\alpha} and its compressibility is \mathrm{\sigma.}

Option: 1

\mathrm{\frac{\sigma P}{\alpha}}


Option: 2

\mathrm{\frac{\alpha P}{\sigma}}


Option: 3

\mathrm{\alpha \sigma P}


Option: 4

\mathrm{\frac{P}{\alpha \sigma}}


Answers (1)

best_answer

Let V be the original volume of the sphere. The decrease in volume under excess pressure P is

                      \mathrm{ \Delta V=\frac{V P}{B}=\sigma V P \quad\left(\because \sigma=\frac{1}{B}\right) }
where B is the bulk modulus. Let \Delta T be the increase in temperature to compensate for this increase in volume.
Then

                                     \mathrm{ \Delta V=\alpha V \Delta T }

Equating the two expression of \mathrm{\Delta V}, we get \mathrm{\Delta T=\frac{\sigma P}{\alpha}}

So the correct choice is (a).

Posted by

Rishabh

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