Heat And Thermodynamics - Mechanics - Physics Previous Year Questions

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 \(=9000 \mathrm{~kg} / \mathrm{m}^{3}\) )

In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final temperature of the mixture.

In a dark room with ambient temperature $\mathrm{T}_0$, a black body is kept at a temperature T . Keeping the temperature of the black body constant (at T), sunrays are allowed to fall on the black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statement(s) is/are correct?

Heat given to the processes is positive. Match Column I with Column II:

The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

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

STATEMENT 1

The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.

Because

STATEMENT 2

The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

An ideal gas is expanding such that PT\(^2\) = constant. The coefficient of volume expansion of the gas is

Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

\(C_V\) and \(C_P\) denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

The figure shows the PV plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then,

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II:

A metal rod AB of length 10x has its one end A in ice at 0\(^\circ\)C and the other end B in water at 100\(^\circ\)C. If a point P on the rod is maintained at 400\(^\circ\)C, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of \(\lambda x\) from the ice end A, find the value of \(\lambda\). (Neglect any heat loss to the surrounding.)

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P₀. Choose the correct option(s) from the following: