Question

In an adiabatic expansion of air, the volume is increased by 6.2%. The percentage change in pressure is (\( \gamma = 1.4 \))

• A. 8.68
• B. 4.84
• C. 6.48
• D. 2.24

Hint:

For adiabatic processes, remember that the relationship between pressure and volume is governed by the equation \( P_1 V_1^\gamma = P_2 V_2^\gamma \). Use this for calculating changes in pressure or volume during adiabatic expansion or compression.

Answer 1

The Correct Option is A

In an adiabatic process, the relation between the pressure and volume is given by the equation: \[ P_1 V_1^\gamma = P_2 V_2^\gamma \] where: - \( P_1, V_1 \) are the initial pressure and volume - \( P_2, V_2 \) are the final pressure and volume - \( \gamma \) is the adiabatic index (given as 1.4 in this case) Since the volume increases by 6.2%, we can express the final volume as: \[ V_2 = V_1(1 + 0.062) \] Now, from the adiabatic relation, we have: \[ \frac{P_2}{P_1} = \left(\frac{V_1}{V_2}\right)^\gamma \] Substituting \( V_2 = V_1(1 + 0.062) \), we get: \[ \frac{P_2}{P_1} = \left(\frac{1}{1 + 0.062}\right)^{1.4} \] Calculating the above expression: \[ \frac{P_2}{P_1} = \left(\frac{1}{1.062}\right)^{1.4} = 0.919^{1.4} = 0.863 \] The percentage change in pressure is: \[ \text{Percentage change} = \left(1 - 0.863\right) \times 100 = 8.68% \] Thus, the percentage change in pressure is 8.68%.