Question

Find the isentropic compressibility of an ideal gas with an adiabatic index of \(1.4\) at a pressure of \(1\) atm.

• A. \(\dfrac{1}{1.4}\ \text{atm}^{-1}\)
• B. \(1.4\ \text{atm}^{-1}\)
• C. \(1\ \text{atm}^{-1}\)
• D. \(0.4\ \text{atm}^{-1}\)

Hint:

For an ideal gas, \[ \boxed{ \beta_s=\frac{1}{\gamma P} } \] where \(\beta_s\) is the isentropic compressibility.

Answer 1

The Correct Option is A

Step 1: Recall the formula for isentropic compressibility. The isentropic compressibility of an ideal gas is \[ \boxed{ \beta_s=\frac{1}{\gamma P}, } \] where
• \(\gamma\) = adiabatic index,
• \(P\) = pressure.

Step 2: Substitute the given values. Given, \[ \gamma=1.4, \] \[ P=1\ \text{atm}. \] Hence, \[ \beta_s = \frac{1}{1.4\times1} = \frac{1}{1.4}\ \text{atm}^{-1}. \] Therefore, \[ \boxed{\frac{1}{1.4}\ \text{atm}^{-1}} \] is the correct answer. Thus, \[ \boxed{(A)} \] is the correct answer.