Thermodynamics PYQ

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q : \Delta U : \Delta W$ is _______.

In the following $p-V$ diagram the equation of state along the curved path is given by $(V-2)^{2}=4 a p$ where $a$ is a constant. The total work done in the closed path is 

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 = $ constant. The coefficient of volume expansion of the gas is _______.

The volume of an ideal gas increases 8 times and temperature becomes $(1 / 4)^{\text {th }}$ of initial temperature during a reversible change. If there is no exchange of heat in this process $(\Delta \mathrm{Q}=0)$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases):

10 mole of oxygen is heated at constant volume from $30^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The change in the internal energy of the gas is $\_\_\_\_$ cal. (The molecular specific heat of oxygen at constant pressure, $C_{P}=7 \mathrm{cal} / \mathrm{mol}.{ }^{\circ} \mathrm{C}$ and $\mathrm{R}=2 \mathrm{cal} / \mathrm{mol}.{ }^{\circ} \mathrm{C}$.)

A certain gas is isothermally compressed to $\left(\dfrac{1}{3}\right)^{rd}$ of its initial volume ($V_o = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5$ N/m$^2$, the magnitude of work done on the gas is _______ J.

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ} \mathrm{C}$ to $87^{\circ} \mathrm{C}$. The rate of consumption of the gas is $\_\_\_\_$ $\mathrm{g} / \mathrm{s}$. (Take heat of combustion of gas $=5.0 \times 10^{4} \mathrm{~J} / \mathrm{g}$) specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$

The r.m.s. speed of oxygen molecules at $47^{\circ} \mathrm{C}$ is equal to that of the hydrogen molecules kept at $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$. (Mass of oxygen molecule/mass of hydrogen molecule $=32 / 2$)

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V, T$. Heating is started from left side until pressure changes to $\dfrac{27P}{8}$. If initial volume of each compartment was $9$ litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas $C_P/C_V = 1.5$)

10 kg of ice at $-10^{\circ} \mathrm{C}$ is added to 100 kg of water to lower its temperature from 25 ${ }^{\circ} \mathrm{C}$. Consider no heat exchange to surroundings. The decrement to the temperature of water is $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$. (specific heat of ice $=2100 \mathrm{~J} / \mathrm{Kg}.{ }^{\circ} \mathrm{C}$, specific heat of water $=4200 \mathrm{~J} / \mathrm{Kg}.{ }^{\circ} \mathrm{C}$, latent heat of fusion of ice $=3.36 \times 10^{5} \mathrm{~J} / \mathrm{Kg}$)

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is _____.

A thermodynamic system is taken through the cyclic process $A B C$ as shown in the figure. The total work done by the system during the cycle $A B C$ is $\_\_\_\_$ J. 

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$ ?

The heat extracted out of $x$ gram of water initially at $50°C$ to cool it down to $0°C$ is sufficient to evaporate $(1000 - x)$ gram of water also initially at $50°C$. The value of $x$ (closest integer) is _______. (Take latent heat of water $2256\text{ kJ/kg.K}$, specific heat capacity of water $4200\text{ J/kg.K}$)

$5$ moles of unknown gas is heated at constant volume from $10 \, °C$ to $20 \, °C$. The molar specific heat of this gas at constant pressure $c_p = 8$ cal/mol.°C and $R = 8.36$ J/mol.°C. The change in the internal energy of the gas is _______ calorie.

A brass wire of length 2 m and radius 1 mm at $27^{\circ} \mathrm{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^{\circ} \mathrm{C}$ creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4 T$, is $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$.

Density of water at $4{ }^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$ are $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and $998 \mathrm{~kg} / \mathrm{m}^{3}$ respectively. The increase in internal energy of 4 kg of water when it is heated from $4{ }^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$ is $\_\_\_\_$ J. (specific heat capacity of water $=4.2 \mathrm{~J} / \mathrm{kg}$. and 1 atmospheric pressure $=10^{5} \mathrm{~Pa}$)

A diatomic gas $(\gamma=1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas $\_\_\_\_$ J.

A cylindrical tube $A B$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $A B$ and passing through the edge at end $A$, as shown in the figure. If $P_{A}$ and $P_{B}$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube) 

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If the average kinetic energy of $H_2$ and $O_2$ molecules, kept in two different sized containers are same, then their temperatures will be same. Reason R: The r.m.s. speed of $H_2$ and $O_2$ molecules are same at same temperature. Choose the correct answer from the options given below

Consider the following statements: A. Zeroth law of thermodynamics gives concept of temperature B. First law of thermodynamics gives concept of internal energy C. In isothermal expansion of ideal gas, $\Delta Q \neq \Delta W$ D. Product of intensive and extensive variables is extensive E. The ratio of any extensive variable to mass will be an extensive variable Choose the correct combination of statements from the options given below:

An ideal gas undergoes an isothermal expansion. Which of the following is true?

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^{\circ} \mathrm{C}$. The gas is now heated to double its temperature. The modified pressure is $\_\_\_\_$ Pa. Note: Volume is constant.

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C}$ respectively. Given the thermal conductivity of $\operatorname{rod} x$ is three times of that of $\operatorname{rod} y$, the temperature at junction points $B$ and $E$ are (close to):