An ideal gas at $0^\circ ext{C}$ and atmospheric pressure $P$ has volume $V$. The percentage increase in its

Question

An ideal gas at $0^\circ	ext{C}$ and atmospheric pressure $P$ has volume $V$. The percentage increase in its temperature needed to expand it to $3V$ at constant pressure is:

Accepted Answer

According to Charles's Law, for an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature ($V \propto T$).

1.  **Initial State:** $V_1 = V$, $T_1 = 0^\circ	ext{C} = 273 	ext{ K}$.
2.  **Final State:** The volume expands to $3V$. Since $V \propto T$, if the volume becomes 3 times the initial volume, the absolute temperature must also become 3 times the initial temperature.
    $T_2 = 3T_1 = 3 	imes 273 = 819 	ext{ K}$.
3.  **Calculate Increase:**
    Change in temperature $\Delta T = T_2 - T_1 = 3T_1 - T_1 = 2T_1$.
4.  **Percentage Increase:**
    $\% 	ext{ Increase} = \frac{\Delta T}{T_1} 	imes 100 = \frac{2T_1}{T_1} 	imes 100 = 200\%$.

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