Question

(b) let (p) and (v) represent the pressure and volume of the (xe(g)) in the container in diagram 3. if a piston is used to reduce the volume of the gas to (\frac{v}{2}) at a constant temperature, what is the new pressure in the container in terms of the original pressure, (p)? (c) describe what happens to the average speed of the (xe) atoms in the container in diagram 3 as the original volume (v) is reduced to (\frac{v}{2}) at a constant temperature. explain.

Explanation:

Step1: Recall Boyle's Law

Boyle's law states that for a given mass of gas at constant temperature, $P_1V_1 = P_2V_2$. Here, $P_1 = P$, $V_1=V$, and $V_2=\frac{V}{2}$.

Step2: Solve for new pressure

Substitute the values into the formula: $P\times V=P_2\times\frac{V}{2}$. Solving for $P_2$ gives $P_2 = 2P$.

for part (c):
The average speed of gas atoms is related to the temperature of the gas. The kinetic - molecular theory states that the average kinetic energy of gas molecules is directly proportional to the absolute temperature ($KE_{avg}=\frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the temperature). Since the temperature is constant when the volume is reduced from $V$ to $\frac{V}{2}$, the average kinetic energy of the Xe atoms remains the same. And since $KE=\frac{1}{2}mv^{2}$, if the average kinetic energy ($KE_{avg}$) is constant and the mass ($m$) of the Xe atoms is constant, the average speed ($v_{avg}$) of the Xe atoms remains the same.

Answer:

$2P$