An insulated cylindrical vessel filled with an insulated piston of negligible weight and negligible…

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
  1. $13.65$
  2. $27.3$
  3. $38.6$
  4. $64.6$

Solution

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 $L=27.3 \mathrm{~cm}$

Asked in: AP EAMCET 2011

Practice more Mechanical Properties of Fluids questions on Aicharya