A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface, as shown in the figure. The atmospheric pressure is $P_0$.
The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is $$\rho$$. In equilibrium, the height H of the water column in the cylinder satisfies
Heat given to the processes is positive. Match Column I with Column II:
| Column I | Column II | ||
|---|---|---|---|
| (A) | JK | (P) | $$ \Delta W>0 $$ |
| (B) | KL | (Q) | $$ \Delta \mathrm{Q}<0 $$ |
| (C) | LM | (R) | $$ \Delta \mathrm{W}<0 $$ |
| (D) | MJ | (S) | $$ \Delta Q>0 $$ |
A cylinder of mass $$1 \mathrm{~kg}$$ is given heat of $$20000 \mathrm{~J}$$ at atmospheric pressure. If initially temperature of cylinder is $$20^{\circ} \mathrm{C}$$, find
(A) The final temperature of the cylinder;
(B) The work done by the cylinder;
(C) The change in internal energy of the cylinder.
Given :
The specific heat of cylinder
$$=400 \mathrm{~J} \mathrm{~kg}^{-1 \circ} \mathrm{C}^{-1}$$
Coefficient of volume expansion
$$=9 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1} \text {; }$$
Atmospheric pressure $$=10^{5} \mathrm{~N} / \mathrm{m}^{2}$$ Density of cylinder $$=9000 \mathrm{~kg} / \mathrm{m}^{3}$$ )
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