A closed hollow insulated cylinder is filled with gas at $${0^ \circ }C$$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to $${100^ \circ }C.$$ If the piston moves $$5\,cm,$$ the length of the hollow cylinder is
A.
$$13.65\,cm$$
B.
$$27.3\,cm$$
C.
$$38.6\,cm$$
D.
$$64.6\,cm$$
Answer :
$$64.6\,cm$$
Solution :
Using Charle's law, we have $$\frac{V}{T} = {\text{constant}}$$
$$ \Rightarrow \frac{{\frac{l}{2} + 5}}{{373}} = \frac{{\frac{l}{2} - 5}}{{273}}$$
As the piston moves $$5\,cm,$$ the length of one side will be $$\left( {\frac{l}{2} + 5} \right)$$ and other side $$\left( {\frac{l}{2} - 5} \right).$$ On solving this equation, we get $$l = 64.6\,cm.$$
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