Thermodynamics PYQ — Page 6

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. 

If three moles of monoatomic gas $(\gamma =\frac{5}{3})$ is mixed with two moles of a diatomic gas $(\gamma =\frac{7}{5})$, the value of adiabatic exponent $\gamma$ for the mixture is:

A diatomic gas $(\gamma=1.4)$ does $100 \mathrm{~J}$ of work in an isobaric expansion. The heat given to the gas is :

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}$ for the gas is :

The parameter that remains the same for molecules of all gases at a given temperature is :

$N$ moles of a polyatomic gas$(f=6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $N$ is:

At room temperature $\left(27^{\circ} \mathrm{C}\right)$, the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$. The temperature of the element, when its resistance is $62 \Omega$, is _____ ${ }^{\circ} \mathrm{C}$.

The specific heat at constant pressure of a real gas obeying $P V^2=R T$ equation is:

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400^{\circ} \mathrm{C}$, the resistance of platinum wire 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: 

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

Let ${\gamma }_{1}$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and ${\gamma }_{2}$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $\frac{{\gamma }_{1}}{{\gamma }_{2}}$ is:

The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between upper fixed point and lower fixed point there are $150$ equal divisions of scale $P$ and $100$ divisions on scale $Q$. The relationship for conversion between the two scales is given by : .

For an ideal gas undergoing isothermal process

For an ideal gas, Cp - Cv is equal to:

A gas is compressed adiabatically, which one of the following statement is NOT true?

$1g$ of a liquid is converted to vapour at $3\times {10}^{5}\mathrm{Pa}$ pressure. If $10%$ of the heat supplied is used for increasing the volume by $1600{\mathrm{cm}}^{3}$ during this phase change, then the increase in internal energy in the process will be :

For three low density gases $A,B,C$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure  The temperature corresponding to the point $'K'$ is:

Given below are two statements: Statement I: The temperature of a gas is $-73^{\circ}C$. When the gas is heated to $527^{\circ}C$, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below:

The pressure $(P)$ and temperature $(T)$ relationship of an ideal gas obeys the equation $P{T}^{2}=$ constant. The volume expansion coefficient of the gas will be :

A faulty thermometer reads $5^{\circ}C$ in melting ice and $95^{\circ}C$ in steam. The correct temperature on absolute scale will be ______ $K$ when the faulty thermometer reads $41^{\circ}C$.

$1\mathrm{kg}$ of water at $100^{\circ}C$ is converted into steam at $100^{\circ}C$ by boiling at atmospheric pressure. The volume of water changes from $1.00\times {10}^{-3}{m}^{3}$ as a liquid to $1.671{m}^{3}$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation $=2257\mathrm{kJ}/\mathrm{kg}$, Atmospheric pressure $=1\times {10}^{5}\mathrm{Pa})$

A water heater of power $2000W$ is used to heat water. The specific heat capacity of water is $4200J{\mathrm{kg}}^{-1}{K}^{-1}$. The efficiency of heater is $70%$. Time required to heat $2\mathrm{kg}$ of water from $10^{\circ}C$ to $60^{\circ}C$ is _____ $s$. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Heat energy of $184\mathrm{kJ}$ is given to ice of mass $600g$ at $-12^{\circ}C$, Specific heat of ice is $2222.3J{\mathrm{kg}}^{–1}^{\circ}{C}^{–1}$ and latent heat of ice is $336\mathrm{kJ}{\mathrm{kg}}^{–1}$. (A) Final temperature of system will be $0^{\circ}C$ (B) Final temperature of the system will be greater than $0^{\circ}C$ (C) The final system will have a mixture of ice and water in the ratio of $5:1$ (D) The final system will have a mixture of ice and water in the ratio of $1:5$ (E) The final system will have water only Choose the correct answer from the options given below :