Question

question 21 (1 point)
an ideal gas is compressed isothermally to one - third of its initial volume. the resulting pressure be ______.

a) impossible to predict on the basis of this data

b) three times as large as the initial value

c) equal to the initial value

d) less than three times as large as the initial value

e) more than three times as large as the initial value

Explanation:

Step1: Recall Boyle's Law for Isothermal Process

For an ideal gas undergoing an isothermal (constant temperature) process, Boyle's Law states that \( P_1V_1 = P_2V_2 \), where \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure and volume.

Step2: Substitute the Given Volume Relationship

We are given that the final volume \( V_2=\frac{1}{3}V_1 \). Substitute \( V_2 \) into Boyle's Law: \( P_1V_1 = P_2\times\frac{1}{3}V_1 \).

Step3: Solve for \( P_2 \)

Divide both sides of the equation by \( V_1 \) (assuming \( V_1
eq0 \), which is valid for a gas volume) to get \( P_1 = \frac{P_2}{3} \). Then multiply both sides by 3: \( P_2 = 3P_1 \). This means the final pressure is three times the initial pressure.

Answer:

b) three times as large as the initial value