Mechanical Properties of Solids

JEE Main level, single correct, medium

92 of 118

Question 92 of 118

Under isothermal condition, the pressure of a gas is given by P=aV–3,P=a{V}^{–3}, where aa is a constant and VV is the volume of the gas. The bulk modulus at constant temperature is equal to

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Answer: (A) 3P3P

The data given is
P=aV−3P=a{V}^{-3}
Bulk modulus is given by,
B=−dPdVV=−VdPdVB=-\dfrac{dP}{\dfrac{dV}{V}}=-V\dfrac{dP}{dV}
=−VddV{aV3}=-V\dfrac{d}{dV}\left\{\dfrac{a}{{V}^{3}}\right\}
=−V[−3aV4]=-V\left[\dfrac{-3a}{{V}^{4}}\right]
=3aV3=3P=\dfrac{3a}{{V}^{3}}=3P

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