Chapter 10, Problem 10.20VP

Interpretation Introduction

To find:

a) Describe the changes in $T,V, n$ and/or $P$ represented by each arrow.

b)  Explain why pressure does not change during the $\left[E\right]\to \left[B\right], \left[E\right]\to \left[F\right], \left[E\right]\to \left[I\right]$ transitions.

c) Explain why the pressure is decreased during $\left[E\right]\to \left[A\right]. \left[E\right]\to \left[C\right], \left[E\right]\to \left[G\right]and \left[E\right]\to \left[H\right]$ transitions.

d) Explain why the pressure is increased during the $\left[E\right]\to \left[D\right]$ transition.

e) Explain if the root-mean-square speed of the molecule in the $\left[E\right]$ cylinder increases, decreases, or remains the same in the $\left[E\right]\to \left[A\right]$ transition.

f) Explain why the molecules in $\left[E\right] or \left[I\right]$ are moving with more root-mean-square speed.

Answer to Problem 10.20VP

Solution:

a)

In transition $\left[E\right]\to \left[A\right]$, $P$ decreases, $V$ increases.

In transition $\left[E\right]\to \left[B\right]$, $T$ decreases, $V$ decreases.

In transition $\left[E\right]\to \left[C\right]$, $P$ decreases, $T$ decreases, and $V$increases.

In transition $\left[E\right]\to \left[D\right]$, $P$ increases, $T$ increases.

In transition $\left[E\right]\to \left[F\right]$, $n$ increases, $V$ increases.

In transition $\left[E\right]\to \left[G\right]$, $n$ decreases, $V$ decreases.

In transition $\left[E\right]\to \left[H\right]$, $P$ decreases, $T$ decreases.

In transition $\left[E\right]\to \left[I\right]$, $V$ increases, $T$ increases.

b) If $T$ decreases, $V$ also decreases, therefore, the pressure does not change for transition $\left[E\right]\to \left[B\right].$ For transition $\left[E\right]\to \left[I\right],$ $T$ increases, $V$ increases.Therefore, pressure does not change. According to Avogadro’s law, $n$ increases, $V$ increases. Therefore, the pressure for transition $\left[E\right]\to \left[F\right]$ does not change.

c) In transitions $\left[E\right]\to \left[A\right]$ and $\left[E\right]\to \left[G\right]$, volume increases. Therefore, it will decrease the pressure. According to the Amonton’s law, if temperature decreases, it will decrease the pressure for transitions $\left[E\right]\to \left[C\right]$ and $\left[E\right]\to \left[H\right]$.

d) Temperature is increasing. Therefore, it will increase the pressure for $\left[E\right]\to \left[D\right]$ transition.

e) In $\left[E\right]\to \left[A\right]$ transition, there is no change in temperature. Therefore, root-mean-square speed of molecules remains the same.

f) More molecules are moving at the root-mean-square speed in [E].

Explanation of Solution

a) As per gas laws:

In transition $\left[E\right]\to \left[A\right]$, $P$ decreases, $V$ increases.

In transition $\left[E\right]\to \left[B\right]$, $T$ decreases, $V$ decreases.

In transition $\left[E\right]\to \left[C\right]$, $P$ decreases, $T$ decreases, and $V increases$.

In transition $\left[E\right]\to \left[D\right]$, $P$ increases, $T$ increases.

In transition $\left[E\right]\to \left[F\right]$, $n$ increases, $V$ increases.

In transition $\left[E\right]\to \left[G\right]$, $n$ decreases, $V$ decreases.

In transition $\left[E\right]\to \left[H\right]$, $P$ decreases, $T$ decreases.

In transition $\left[E\right]\to \left[I\right]$, $V$ increases, $T$ increases.

b) According to Charles’s law,$V\propto T$.

So, if $T$ decreases, $V$ also decreases. Therefore, the pressure does not change for transition $\left[E\right]\to \left[B\right].$ For transition $\left[E\right]\to \left[I\right],$ $T$ increases so $V$ increases. Therefore, the pressure does not change. According to Avogadro’s law, $n$ increases so $V$ increases. Therefore, the pressure for transition $\left[E\right]\to \left[F\right]$ does not change.

c) According to the Boyle’s law,$P\propto V$. In transitions $\left[E\right]\to \left[A\right]$ and $\left[E\right]\to \left[G\right]$, volume increases. Therefore, it will decrease the pressure. According to the Amonton’s law, if temperature decreases, it will decrease the pressure for transitions $\left[E\right]\to \left[C\right]$ and $\left[E\right]\to \left[H\right]$.

d) According to the Amonton’s law, temperature is increasing. Therefore, it will increase the pressure for $\left[E\right]\to \left[D\right]$ transition.

e) In $\left[E\right]\to \left[A\right]$ transition, there is no change in the temperature. Therefore, the root-mean-square speed of molecules remains the same.

f) The fraction of molecules moving at the root-mean-square speed increases as the temperature decreases. So, more molecules are moving at the root-mean-square speed in [E].

Conclusion:

We use the changes in each given transition and different gas laws to find out the changes in pressure, volume, moles, and temperature in all transitions.