Thermodynamics PYQ — Page 4

Consider a rectangular sheet of solid material of length $\ell=9 \mathrm{~cm}$ and width $\mathrm{d}=4 \mathrm{~cm}$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $\mathrm{m}=0.1 \mathrm{~kg}$ and the specific heat capacity $\mathrm{C}_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \mathrm{~J}$ then change in area of the rectangular sheet is :-

$$ \text{Match the LIST-I with LIST-II} $$ \[ \begin{array}{|l|p{6cm}|l|p{4cm}|} \hline \textbf{LIST-I} & & \textbf{LIST-II} & \\ \hline A. & \text{Pressure varies inversely with volume of an ideal gas.} & I. & \text{Adiabatic process} \\ \hline B. & \text{Heat absorbed goes partly to increase internal energy and partly to do work.} & II. & \text{Isochoric process} \\ \hline C. & \text{Heat is neither absorbed nor released by a system.} & III. & \text{Isothermal process} \\ \hline D. & \text{No work is done on or by a gas.} & IV. & \text{Isobaric process} \\ \hline \end{array} \] $$ \text{Choose the correct answer from the options given below:} $$

An ideal gas initially at $0^{\circ} \mathrm{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3 / 2$, the change in temperature due to the thermodynamic process is _____ K.

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ $\times 10^{-1} \mathrm{~J}$. (Take $\pi=3.14$) 

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:

An ideal gas exists in a state with pressure $P_0$ volume $\mathrm{V}_0$.It is isothermally expanded to 4 times of its initial volume $\left(\mathrm{V}_0\right)$, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is :

An amount of ice of mass $10^{-3} \mathrm{~kg}$ and temperature $-10^{\circ} \mathrm{C}$ is transformed to vapour of temperature $110^{\circ} \mathrm{C}$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat of water $=4180 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat of steam $=1920 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, Latent heat of ice $=3.35 \times 10^5 \mathrm{Jkg}^{-1}$ and Latent heat of steam $=2.25 \times 10^6$ $\mathrm{Jkg}^{-1}$ )

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^{\circ} \mathrm{C}$ and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x=$_______ (Given $\sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14$ and assume that the emissivity of wire material is same at all wavelength.)

A monoatomic gas having $\gamma=\frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial volume. The ratio of final pressure and initial pressure is: ( $\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is $\qquad$ grams. (Latent heat of fusion of lead $=2.5 \times 10^4 \mathrm{JKg}^{-1}$ and specific heat capacity of lead $=125 \mathrm{JKg}^{-1}$ $\left.\mathrm{K}^{-1}\right)$

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is : (Take $\gamma=1.5: \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

A cup of coffee cools from $90^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ in t minutes when the room temperature is $20^{\circ} \mathrm{C}$. The time taken by the similar cup of coffee to cool from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ at the same room temperature is :

A container of fixed volume contains a gas at \(27^{\circ} \mathrm{C}\). To double the pressure of the gas, the temperature of gas should be raised to ______ \({ }^{\circ} \mathrm{C}\).

A Carnot engine $(\mathrm{E})$ is working between two temperatures 473 K and 273 K . In a new system two engines - engine $E_1$ works between 473 K to 373 K and engine $E_2$ works between 373 K to 273 K . If $\eta_{12}, \eta_1$ and $\eta_2$ are the efficiencies of the engines $E, E_1$ and $E_2$, respectively, then

Two vessels $A$ and $B$ are of the same size and are at same temperature. $A$ contains $1g$ of hydrogen and $B$ contains $1g$ of oxygen. ${P}_{A}$ and ${P}_{B}$ are the pressures of the gases in $A$ and $B$ respectively, then $\frac{{P}_{A}}{{P}_{B}}$ is :

Two thermodynamical process are shown in the figure. The molar heat capacity for process $A$ and $B$ are ${C}_{A}$ and ${C}_{B}$. The molar heat capacity at constant pressure and constant volume are represented by ${C}_{P}$ and ${C}_{V}$, respectively. Choose the correct statement. 

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is: 

Two conductors have the same resistances at $0^{\circ}C$ but their temperature coefficients of resistance are ${\alpha }_{1}$ and ${\alpha }_{2}$. The respective temperature coefficients for their series and parallel combinations are :

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

The translational degrees of freedom $\left(f_t\right)$ and rotational degrees of freedom $\left(f_r\right)$ of $\mathrm{CH}_4$ molecule are:

The total kinetic energy of $1$ mole of oxygen at $27^{\circ}C$ is : [Use universal gas constant $(R)=8.31J{\mathrm{mol}}^{-1}{K}^{-1}$ ]

The temperature of a gas is $-78^{\circ} \mathrm{C}$ and the average translational kinetic energy of its molecules is $\mathrm{K}$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $2 \mathrm{~K}$ is :

The temperature of a gas having $2.0\times {10}^{25}$ molecules per cubic meter at $1.38\mathrm{atm}$ (Given, $k=1.38\times {10}^{-23}J{K}^{-1})$ is :