QuestionAugust 27, 2025

What will be the temperature of an ideal gas if the volume is halved at constant pressure? Doubled Tripled Halved Unchanged

What will be the temperature of an ideal gas if the volume is halved at constant pressure? Doubled Tripled Halved Unchanged
What will be the temperature of an ideal gas if the volume is halved at constant pressure?
Doubled
Tripled
Halved
Unchanged

Solution
4.0(227 votes)

Answer

Halved Explanation 1. Apply Ideal Gas Law The ideal gas law is given by PV = nRT. At constant pressure, if the volume is halved, we need to find the effect on temperature. 2. Relate Volume and Temperature Using the relation \frac{V_1}{T_1} = \frac{V_2}{T_2} (Charles's Law), where V_2 = \frac{V_1}{2}, solve for T_2. 3. Solve for New Temperature Rearrange to get T_2 = \frac{T_1 \cdot V_2}{V_1} = \frac{T_1 \cdot \frac{V_1}{2}}{V_1} = \frac{T_1}{2}.

Explanation

1. Apply Ideal Gas Law<br /> The ideal gas law is given by $PV = nRT$. At constant pressure, if the volume is halved, we need to find the effect on temperature.<br />2. Relate Volume and Temperature<br /> Using the relation $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (Charles's Law), where $V_2 = \frac{V_1}{2}$, solve for $T_2$.<br />3. Solve for New Temperature<br /> Rearrange to get $T_2 = \frac{T_1 \cdot V_2}{V_1} = \frac{T_1 \cdot \frac{V_1}{2}}{V_1} = \frac{T_1}{2}$.
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