Question

An adiabatic Bulk modulus of an ideal gas at Pressure \(\mathrm{P}\) is (A) \(\gamma \mathrm{P}\) (B) \((\mathrm{p} / \gamma)\) (C) \(\mathrm{P}\) (D) \((\mathrm{p} / 2)\)

Short answer

The short answer is: The adiabatic Bulk modulus of an ideal gas at pressure \(P\) is (A) \(\gamma P\), where \(\gamma\) is the adiabatic index (heat capacity ratio).

Step-by-step solution

Write down the adiabatic bulk modulus formula

The formula for the adiabatic bulk modulus of an ideal gas (\(B_{\text{adiabatic}}\)) in terms of pressure (\(P\)) and adiabatic index (\(\gamma\)) is: \[B_{\text{adiabatic}} = \gamma P\]

Compare the formula with the given options

We will now compare the formula \(B_{\text{adiabatic}} = \gamma P\) with the given options to determine which one is correct: (A) \(\gamma P\) (B) \(\dfrac{P}{\gamma}\) (C) \(P\) (D) \(\dfrac{P}{2}\)

Select the correct option

By comparing the formula \(B_{\text{adiabatic}} = \gamma P\) with the given options, we see that the correct option is (A) \(\gamma P\).