Thermodynamics PYQ — Page 19

Given that $1 \mathrm{~g}$ of water in liquid phase has volume $1 \mathrm{~cm}^3$ and in vapour phase $1671 \mathrm{~cm}^3$ at atmospheric pressure and the latent heat of vaporization of water is $2256 \mathrm{~J} / \mathrm{g}$; the change in the internal energy in joules for $1 \mathrm{~g}$ of water at $373 \mathrm{~K}$ when it changes from liquid phase to vapour phase at the same temperature is :

 The above $P-V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal mono-atomic gas. The amount of heat, extracted from the source in a single cycle, is:

$500 \mathrm{~g}$ of water and $100 \mathrm{~g}$ of ice at $0^{\circ} \mathrm{C}$ are in a calorimeter whose water equivalent is $40 \mathrm{~g} .10 \mathrm{~g}$ of steam at $100^{\circ} \mathrm{C}$ is added to it. Then water in the calorimeter is : (Latent heat of ice $=80 \mathrm{cal} / \mathrm{g}$, Latent heat of steam $=540 \mathrm{cal} / \mathrm{g}$ )

The heat radiated per unit area in 1 hour by a furnace whose temperature is $3000 \mathrm{~K}$ is $(\sigma=5.7 \times$ $10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}$ )

An ideal monatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2 V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2 \mathrm{~V}$, the final pressure is $P_a$. The ratio $\frac{P_a}{P_i}$ is

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: In an adiabatic process, change in internal energy of a gas is equal to work done on/ by the gas in the process. Statement 2: The temperature of a gas remains constant in an adiabatic process.

A wooden wheel of radius $\mathrm{R}$ is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area S and length $L$. $L$ is slightly less than $2 \pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta \mathrm{T}$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Youngs' modulus is $Y$, the force that one part of the wheel applies on the other part is : 

A given ideal gas with $\gamma=\frac{C_p}{C_v}=1.5$ at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

$n$ moles of an ideal gas undergo a process $A \rightarrow B$ as shown in the figure. Maximum temperature of the gas during the process is 

Helium gas goes through a cycle $\mathrm{ABCDA}$ (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas) 

The pressure of an ideal gas varies with volume as $P=\alpha V$, where $\alpha$ is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes ' $m$ ' times its initial volume. The work done by the gas in the process is

A large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $\left(\frac{L}{2}\right)$ each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at $100^{\circ} \mathrm{C}$ and that of steel at $0^{\circ} \mathrm{C}$ then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel)

A perfect gas at $27^{\circ} \mathrm{C}$ is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to

Three perfect gases at absolute temperatures $T_1, T_2$ and $T_3$ are mixed. The masses of molecules are $m_1$, $m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is :

$100 \mathrm{~g}$ of water is heated from $30^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $4148 \mathrm{~J} / \mathrm{kg} / \mathrm{K}$ ):

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :

Two conductors have the same resistance at $0^{\circ} \mathrm{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients of their series and parallel combinations are nearly

A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from $\mathrm{V}$ to $32 \mathrm{~V}$ the efficiency of the engine is

The net work done on the gas in the cycle ABCDA is

One kg of a diatomic gas is at a pressure of $8 \times 10^4 \mathrm{~N} / \mathrm{m}^2$. The density of the gas is $4 \mathrm{~kg} / \mathrm{m}^{-3}$. What is the energy of the gas due to its thermal motion?

Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figure.

The work done on the gas in taking it from $D$ to $A$ is

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_1$ and contains ideal gas at pressure $P_1$ and temperature $T_1$. The other chamber has volume $V_2$ and contains ideal gas at pressure $P_2$ and temperature $T_2$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be