question 15
one mole of argon, ar(g), is heated from 20°c to 30° in a piston container and the volume increases. which parameters, if any, are changed (check all that apply)?
□ v
□ p
□ t
□ n
□ r

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# Brief Explanations:
- **Volume (V)**: The problem states the volume increases, so V changes.
- **Temperature (T)**: The argon is heated from $20^\circ\text{C}$ to $30^\circ\text{C}$, so temperature (T) changes.
- **Pressure (P)**: In a piston - container, if volume increases and temperature increases, for an ideal gas ($PV = nRT$), with $n$ (moles) constant and $R$ (gas constant) constant, when $T$ and $V$ change, $P$ should remain constant? Wait, no—wait, the piston allows volume to change, but if it's a piston, maybe pressure is constant? Wait, no, the problem says "the volume increases" when heated. Wait, let's re - examine: $n = 1$ mole (constant), $R$ is gas constant (constant). The temperature $T$ increases (from $20^\circ\text{C}$ to $30^\circ\text{C}$), volume $V$ increases. For the ideal gas law $PV=nRT$, if $n$ and $R$ are constant, and $T$ and $V$ change, what about $P$? Wait, maybe in a piston, the pressure is equal to the external pressure, so if the piston is free to move, pressure remains constant? But the problem says "the volume increases" when heated. Wait, no—let's think again. The temperature $T$ is changed (heated), so $T$ changes. The volume $V$ is stated to increase, so $V$ changes. The number of moles $n = 1$ mole, so $n$ is constant. $R$ is a gas constant, so $R$ is constant. What about pressure $P$? From $PV=nRT$, if $n$ and $R$ are constant, and $T$ and $V$ both increase, can $P$ stay constant? Let's see: $P=\frac{nRT}{V}$. If $T$ increases and $V$ increases, depending on the ratio of $T$ and $V$ change, but in the case of a gas in a piston (like a cylinder with a movable piston), the pressure is equal to the atmospheric pressure (external pressure), so $P$ is constant. But the problem is asking which parameters are changed. So $T$ is changed (heated), $V$ is changed (volume increases), $P$ is constant (if piston is movable), $n$ is 1 mole (constant), $R$ is constant. Wait, but maybe I made a mistake. Wait, the question is "which parameters, if any, are changed". So:
    - $V$: changed (given "volume increases").
    - $T$: changed (heated from $20^\circ\text{C}$ to $30^\circ\text{C}$).
    - $P$: If it's a piston - cylinder with a movable piston, pressure is constant (equal to external pressure), so $P$ is not changed? Wait, no—maybe the piston is not necessarily at constant pressure. Wait, the problem doesn't state that pressure is constant. Let's re - read the problem: "One mole of argon, Ar(g), is heated from $20^\circ\text{C}$ to $30^\circ$ in a piston container and the volume increases." So heating (change in $T$) and volume increase (change in $V$). So $T$ changes, $V$ changes. $n = 1$ mole (constant), $R$ is constant. What about $P$? From $PV=nRT$, $P=\frac{nRT}{V}$. If $T$ increases and $V$ increases, the change in $P$ depends on the relative change of $T$ and $V$. But maybe in the context of this question, they consider that $T$ and $V$ are changed, $P$ is constant, $n$ is constant, $R$ is constant. So the changed parameters are $V$ and $T$. Wait, but maybe the question considers that when you heat a gas in a piston (movable), pressure is constant, but $T$ and $V$ change. So $V$ (changed), $T$ (changed), $P$ (constant), $n$ (constant), $R$ (constant). So the parameters changed are $V$ and $T$.
# Answer:
- $V$ (Volume) is changed (as volume increases).
- $T$ (Temperature) is changed (as it is heated from $20^\circ\text{C}$ to $30^\circ\text{C}$).
- $P$ (Pressure): If the piston is movable, pressure is constant (equal to external pressure), so $P$ is not changed.
- $n$ (moles): 1 mole, so $n$ is constant.
- $R$ (gas constant): Constant.

So the parameters that are changed are $V$ and $T$. So the checkboxes for $V$ and $T$ should be checked.

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