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At constant temperature, a gas of volume 20 cc is compressed until its pressure becomes four times the original. What is the new volume?
A$80\ \text{cc}$
B$10\ \text{cc}$
C$5\ \text{cc}$
D$16\ \text{cc}$
Answer & Solution
Correct answer: C. $5\ \text{cc}$
1. At constant temperature Boyle's law gives $P_1 V_1 = P_2 V_2$.
2. With $P_2 = 4P_1$: $V_2 = \dfrac{P_1}{P_2}\,V_1 = \dfrac{P_1}{4P_1}\times 20$.
3. Simplify: $V_2 = \dfrac{20}{4} = 5$ cc.
4. Higher pressure must give smaller volume, so the answer is below 20 cc.
5. The value 80 cc multiplies instead of dividing, the classic inverse-relation trap.
_Source: Samacheer Kalvi (TN SCERT) Class 10 Science, Unit 3 Thermal Physics "Solved Problems", p.45_
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