Question:
At 30°C, 2 moles gas expands adiabatically from V to 4V. Final temperature is:
At 30°C, 2 moles gas expands adiabatically from V to 4V. Final temperature is:
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In adiabatic expansion, temperature drops rapidly as volume increases.
Updated On: Jul 18, 2026
- 150 K
- 100 K
- 120 K
- 140 K
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The Correct Option is C
Solution and Explanation
Step 1: Convert temperature.
\[ T_1 = 303K \]
Step 2: Adiabatic law.
\[ TV^{\gamma-1} = const \]
Step 3: Apply relation.
\[ T_2 = T_1 \left(\frac{V}{4V}\right)^{2/3} \]
Step 4: Simplify.
\[ T_2 = \frac{303}{2^{4/3}} \]
Step 5: Approximation.
\[ 2^{4/3} \approx 2.52 \Rightarrow T_2 \approx 120K \]
Step 6: Final answer.
\[ \boxed{120K} \]
\[ T_1 = 303K \]
Step 2: Adiabatic law.
\[ TV^{\gamma-1} = const \]
Step 3: Apply relation.
\[ T_2 = T_1 \left(\frac{V}{4V}\right)^{2/3} \]
Step 4: Simplify.
\[ T_2 = \frac{303}{2^{4/3}} \]
Step 5: Approximation.
\[ 2^{4/3} \approx 2.52 \Rightarrow T_2 \approx 120K \]
Step 6: Final answer.
\[ \boxed{120K} \]
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