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An insulated cylindrical vessel filled with an insulated piston of negligible weight and negligible thickness at the mid point of the vessel. The cylinder contains a gas at $0^{\circ} \mathrm{C}$. When the gas is heated to $100^{\circ} \mathrm{C}$, the piston moves through a length of $5 \mathrm{~cm}$. Length of the cylindrical vessel in $\mathrm{cm}$ is
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The correct answer is:
$27.3$
According to question,
$\begin{array}{rlrl} & \therefore & \frac{273}{L / 2} & =\frac{373}{(L / 2)+5} \\ \Rightarrow & 273\left(\frac{L}{2}+5\right) & =373\left(\frac{L}{2}\right)\end{array}$
or $\quad 273 \times 5=100\left(\frac{L}{2}\right)$
or $L=27.3 \mathrm{~cm}$
$\begin{array}{rlrl} & \therefore & \frac{273}{L / 2} & =\frac{373}{(L / 2)+5} \\ \Rightarrow & 273\left(\frac{L}{2}+5\right) & =373\left(\frac{L}{2}\right)\end{array}$
or $\quad 273 \times 5=100\left(\frac{L}{2}\right)$
or $L=27.3 \mathrm{~cm}$
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