Question

The isothermal bulk modulus of an ideal gas at pressure p is

Answer 1

Explanation: 

Isothermal bulk modulus is defined as volume times negative partial derivative of pressure with respect to volume at constant temperature: 
K = - V ∙ (∂P/∂V)_T 

An ideal gas satisfies the following equation of state: 
P∙V = n∙R∙T 

So the pressure for an ideal gas is given by: 
P = n∙R∙T/V 
The partial derivative of pressure w.r.t. volume at constant temperature is: 
(∂P/∂V)_T = (∂(n∙R∙T/V)/∂P)_T 
= n∙R∙T ∙ d(1/V)/dV 
= - n∙R∙T/V² 
= (- n∙R∙T/V) ∙ (1/V) 
= - P/V 

Hence, 
K = - V ∙ ( - P/V ) = P