JEE Main 2017 — Thermodynamics

A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, A its area of cross-section, $Y$ its Young's modulus, and $\alpha$ its coefficient of linear expansion. Then, $F$ is equal to:

A copper ball of mass $100 \text{g}$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100 \text{g,}$ filled with $170 \text{g}$ of water at room temperature. Subsequently, the temperature of the system is found to be $75^{\circ}C$. $T$ is given by: (Given: room temperature $=30^{\circ}C$, specific heat of copper $=0.1 \mathrm{cal}{g}^{-1} ^{\circ}{C}^{-1}$)

A steel rail of length $5m$ and area of cross section $40 {\mathrm{cm}}^{2}$ is prevented from expanding along its length while the temperature rises by $10^{\circ}C$ . If coefficient of linear expansion and Young's modulus of steel are $1.2\times {10}^{-5} {K}^{-1}$ and $2\times {10}^{11} N{m}^{-2}$ respectively, the force developed in the rail is approximately:

An engine operates by taking $n$moles of an ideal gas through the cycle $ABCDA$ shown in figure. The thermal efficiency of the engine is: (Take ${C}_{v}=1.5R$, where$R$ is gas constant) 

An external pressure $P$ is applied on a cube at $0^{\circ}C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

An ideal gas has molecules with $5$ degrees of freedom. The ratio of specific heats at constant pressure $({C}_{p})$ and at constant volume $({C}_{V})$ is:

${C}_{p}-{C}_{v}=\frac{R}{M}$ and ${C}_{v}$ are specific heats at constant pressure and constant volume respectively. It is observed that, ${C}_{p}-{C}_{v}=a$ for hydrogen gas and ${C}_{p}-{C}_{v}=b$ for nitrogen gas. The correct relation between $a$ and $b$ is:

For the $P-V$ diagram given for an ideal gas  Out of the following which one correctly represents the $T-P$ diagram?

In an experiment, a sphere of aluminium of mass $0.20\mathrm{kg}$ is heated up to $150^{\circ}C$ . Immediately, it is put into water of volume $150\mathrm{cc}$at ${27}^{o}C$ kept in a calorimeter of water equivalent to$0.025\mathrm{kg}$ . The final temperature of the system is ${40}^{o}C$ . The specific heat of the aluminium is(take $4.2\mathrm{Joule}=1\mathrm{calorie}$ )

$N$ moles of diatomic gas in a cylinder is at a temperature $T$. Heat is supplied to the cylinder such that the temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. The change in the total kinetic energy of the gas is

The temperature of an open room of volume $30{m}^{3}$ increases from $17^{\circ}C$ to $27^{\circ}C$ due to the sunshine. The atmospheric pressure in the room remains $1\times {10}^{5}\mathrm{Pa}$. If ${n}_{i}$ and ${n}_{f}$ are the number of molecules in the room before and after heating, then ${n}_{f}-{n}_{i}$ will be: