Question:
Gas heated so rms speed doubles. Heat added = ?
Gas heated so rms speed doubles. Heat added = ?
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Doubling rms speed means temperature becomes 4 times.
Updated On: Jul 18, 2026
- 34.5 kJ
- 12.6 kJ
- 1.8 kJ
- 22.4 kJ
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The Correct Option is D
Solution and Explanation
Step 1: rms relation.
\[ v \propto \sqrt{T} \Rightarrow T_2 = 4T_1 \]
Step 2: Temperature change.
\[ T_1 = 300K,\quad T_2 = 1200K \]
Step 3: Heat formula.
\[ Q = nC_V\Delta T \]
Step 4: Substitute.
\[ Q = 2 \times \frac{3}{2}R \times 900 \]
Step 5: Compute.
\[ Q = 22410 J \]
Step 6: Final answer.
\[ \boxed{22.4 kJ} \]
\[ v \propto \sqrt{T} \Rightarrow T_2 = 4T_1 \]
Step 2: Temperature change.
\[ T_1 = 300K,\quad T_2 = 1200K \]
Step 3: Heat formula.
\[ Q = nC_V\Delta T \]
Step 4: Substitute.
\[ Q = 2 \times \frac{3}{2}R \times 900 \]
Step 5: Compute.
\[ Q = 22410 J \]
Step 6: Final answer.
\[ \boxed{22.4 kJ} \]
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