Thermodynamics PYQ — Page 17

Two moles of an ideal monoatomic gas occupies a volume $V$ at ${27}^{o}C$ . The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ change in its internal energy.

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:

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:

${C}_{p}-{C}_{v}=\frac{R}{M}$ 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:

$N$ 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

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 $=0.1 \mathrm{cal}{g}^{-1} ^{\circ}{C}^{-1}$)

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:

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:

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 $4.2\mathrm{Joule}=1\mathrm{calorie}$ )

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 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) 

$200g$ water is heated from ${40}^{ o}C$ to ${60}^{ o}C$ . Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water $=4184$ $J{\mathrm{kg}}^{-1}{K}^{-1}$):

$n$ moles of an ideal gas undergoes a process $A\rightarrow B$ as shown in the figure. The maximum temperature of the gas during the process will be: 

Which of the following shows the correct relationship between the pressure $'P'$ and density $\rho$ of an ideal gas at constant temperature ?

A simple pendulum made of a bob of mass m and a metallic wire of a negligible mass has a time period of $2s$ at $T=0^{\circ}C$. If the temperature of the wire is increased, and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope $S$. If the coefficient of linear expansion of metal is $\alpha$, then the value of $S$ is

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

A pendulum clock loses 12 s a day if the temperature is ${40}^{o}$ C and gains 4s a day if the temperature is ${20}^{o}$ C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion $(\alpha )$ of the metal of the pendulum shaft are respectively:

An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $P{V}^{n}=$ constant, then n is given by (Here ${C}_{P}$ and ${C}_{V}$ are molar specific heat at constant pressure and constant volume, respectively) :

A solid body of constant heat capacity $1J{(℃)}^{-1}$ is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same amount of heat. (ii) Sequentially keeping in contact with $8$ reservoirs such that each reservoir supplies the same amount of heat. In both, cases the body is brought from initial temperature $100K$ to final temperature $200K$ . Entropy change of the body in the two cases respectively is: Note: This question was awarded as a bonus since temperatures were given in centigrade instead of in Kelvin. Proper corrections are made in the question to avoid it.

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on $T as {T}^{q}$ . A good estimate for q is:

Using equipartition of energy, the specific heat (in $J {\mathrm{kg}}^{-1} {K}^{-1}$ ) of Aluminium at high temperature can be estimated to be (atomic weight of Aluminium $=27$)

An ideal gas goes through a reversible cycle $a\rightarrow b\rightarrow c\rightarrow d$ has the V - T diagram shown below. Process $d\rightarrow a and b\rightarrow c$ are adiabatic.  The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as ${V}^{q}$ , where $V$ is the volume of the gas. The value of $q$ is: $(\gamma =\frac{{C}_{P}}{{C}_{v}})$