Answer
Verified
89.7k+ views
Hint: Bulk modulus is the measure of the compression of any substance. The bulk modulus is the ratio of infinite pressure increase to the volume of the substance. The reciprocal of the bulk modulus is known as compressibility.
Formula used:
The formula of the ideal gas equation is given by,
$ \Rightarrow PV = nRT$
Where pressure is P, the volume V, the number of moles is n, the universal gas constant is R and the temperature is T.
Complete step by step solution:
It is asked in the problem about the isothermal bulk modulus of an ideal gas at pressure ‘P’.
The formula of the ideal gas equation is given by,
$ \Rightarrow PV = nRT$
Where pressure is P, the volume V, the number of moles is n, the universal gas constant is R and the temperature is T.
Now differentiating the ideal gas equation we get,
$ \Rightarrow \left( {P\Delta V} \right) + \left( {V\Delta P} \right) = 0$
Here it is noted that the$\Delta T = 0$, as the temperature is constant.
$ \Rightarrow \dfrac{{\Delta V}}{V} = - \dfrac{{\Delta P}}{P}$
The isothermal bulk modulus is equal to,
$ \Rightarrow {B_{isothermal}} = - \dfrac{{\Delta P}}{{\left( {\dfrac{{\Delta V}}{V}} \right)}} = P$
So the isothermal bulk modulus with pressure P is equal to P.
The correct answer for this problem is option A.
Additional information: The bulk modulus is represented by the B or K. Mathematically bulk modulus is equal to $B = - V\dfrac{{dP}}{{dV}}$ where pressure is P and volume is V. The isothermal bulk modulus is the bulk modulus of the when temperature is constant.
Note: The isothermal bulk modulus is defined as the ratio of the change in the pressure to the fractional change in the volume at constant temperature. The derivation of the ideal gas gives the isothermal bulk modulus of the material.
Formula used:
The formula of the ideal gas equation is given by,
$ \Rightarrow PV = nRT$
Where pressure is P, the volume V, the number of moles is n, the universal gas constant is R and the temperature is T.
Complete step by step solution:
It is asked in the problem about the isothermal bulk modulus of an ideal gas at pressure ‘P’.
The formula of the ideal gas equation is given by,
$ \Rightarrow PV = nRT$
Where pressure is P, the volume V, the number of moles is n, the universal gas constant is R and the temperature is T.
Now differentiating the ideal gas equation we get,
$ \Rightarrow \left( {P\Delta V} \right) + \left( {V\Delta P} \right) = 0$
Here it is noted that the$\Delta T = 0$, as the temperature is constant.
$ \Rightarrow \dfrac{{\Delta V}}{V} = - \dfrac{{\Delta P}}{P}$
The isothermal bulk modulus is equal to,
$ \Rightarrow {B_{isothermal}} = - \dfrac{{\Delta P}}{{\left( {\dfrac{{\Delta V}}{V}} \right)}} = P$
So the isothermal bulk modulus with pressure P is equal to P.
The correct answer for this problem is option A.
Additional information: The bulk modulus is represented by the B or K. Mathematically bulk modulus is equal to $B = - V\dfrac{{dP}}{{dV}}$ where pressure is P and volume is V. The isothermal bulk modulus is the bulk modulus of the when temperature is constant.
Note: The isothermal bulk modulus is defined as the ratio of the change in the pressure to the fractional change in the volume at constant temperature. The derivation of the ideal gas gives the isothermal bulk modulus of the material.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
Choose the incorrect statement from the following A class 12 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
A pendulum clock keeps the correct time at 20 degrees class 11 physics JEE_Main
Assertion The trajectory of a projectile is quadratic class 11 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
Ethylidene dichloride is obtained by the reaction of class 12 chemistry JEE_Main