Thermodynamics PYQs

An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 J/s, then the rate at which internal energy increases will be:

At a certain temperature T(K), during a process, 500 J is absorbed by the system and work of 200 J is done by the system. Then change in internal energy of the system is:

A container has two chambers of volumes V₁ = 2 litres and V₂ = 3 litres separated by a partition made of a thermal insulator. The chambers contains n₁ = 5 and n₂ = 4 moles of ideal gas at pressures P₁ = 1 atm and P₂ = 2 atm, respectively. When the partition is removed, the equilibrium pressure of the system is:

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B are displaced by $16\,\text{cm}$ and $9\,\text{cm}$, respectively. If the change in their internal energy is the same, then the ratio $\dfrac{r_A}{r_B}$ is equal to

Given below are two statements : Statement I : In ecosystem, there is unidirectional flow of energy of sun from producers to consumers. Statement II : Ecosystems are exempted from 2nd law of thermodynamics. In the light of the above statements, choose the most appropriate answer from the options given below :

A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is:

The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures P₁, P₂ and P₃ compared with those of Charles’s law represented by dotted lines. Then the correct relation is:

A Carnot engine has an efficiency of 50% when the source is at a temperature 327°C. The temperature of the sink is :

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is:

Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is :

The quantities of heat required to raise the temperature of two solid copper spheres of radii r₁ and r₂ (r₁ = 1.5 r₂) through 1 K are in the ratio :

An ideal gas expands isothermally from $10^{-3}\,\text{m}^3$ to $10^{-2}\,\text{m}^3$ at $300\,K$ against a constant pressure of $10^5\,\text{N m}^{-2}$. The work done on the gas is

Reversible expansion of an ideal gas under isothermal and adiabatic conditions are as shown in the figure. AB represents isothermal expansion and AC represents adiabatic expansion. Which of the following options is not correct?

A deep rectangular pond of surface area A, containing water (density = ρ, specific heat capacity = s), is located in a region where the outside air temperature is at a steady value of −26°C. The thickness of the frozen ice layer in this pond, at a certain instant is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of ice layer, at this instant would be given by

1 g of water, of volume 1 cm³ at 100°C, is converted into steam at same temperature under normal atmospheric pressure (= 1 × 10⁵ Pa). The volume of steam formed is 1671 cm³. If the specific latent heat of vaporisation of water is 2256 J/g, the change in internal energy is:

A sample of 0.1 g of water at 100°C and normal pressure (1.013 × 10$^5$ Nm⁻²) requires 54 cal of heat energy to convert it to steam at 100°C. If the volume of the steam produced is 1671 c.c, the change in internal energy of the sample is:

The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is:

The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is:

Thermodynamic processes are indicated in the following diagram.

A Carnot engine having an efficiency of $\dfrac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is $10\ \text{J}$, the amount of energy absorbed from the reservoir at lower temperature is

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at $100^\circ C$, while the other one is at $0^\circ C$. If the two bodies are brought in contact assuming no heat loss, then the final common temperature is:

A body cools from a temperature $3T$ to $2T$ in 10 minutes. The room temperature is $T$. Assume that Newton’s law of cooling is applicable. The temperature of the body at the end of the next 10 minutes will be:

One mole of an ideal monoatomic gas undergoes a process described by the equation $PV^3 = \text{constant}$. The heat capacity of the gas during this process is:

The temperature inside a refrigerator is $t_2^\circ C$ and the room temperature is $t_1^\circ C$. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be:

$4.0\,\text{g}$ sample of a gas occupies $22.4\,\text{L}$ at NTP. The specific heat capacity of the gas at constant volume is $5.0\,\text{JK}^{-1}\text{mol}^{-1}$. If the speed of sound in this gas at NTP is $952\,\text{ms}^{-1}$, then the heat capacity at constant pressure is: (Take gas constant R = 8.3 $\text{JK}^{-1}\text{mol}^{-1}$)

The coefficient of performance of a refrigerator is 5. If the temperature inside the freezer is $-20^\circ\text{C}$, the temperature of the surroundings to which it rejects heat is:

An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas?

Steam at $100^{\circ}\mathrm{C}$ is passed into $20\,\mathrm{g}$ of water at $10^{\circ}\mathrm{C}$. When the water acquires a temperature of $80^{\circ}\mathrm{C}$, the mass of water present will be: (Take specific heat of water $= 1\,\mathrm{cal\,g^{-1}\,^{\circ}C^{-1}}$ and latent heat of steam $= 540\,\mathrm{cal\,g^{-1}}$)

A quantity of water cools from $70^{\circ}\mathrm{C}$ to $60^{\circ}\mathrm{C}$ in the first $5$ minutes and to $54^{\circ}\mathrm{C}$ in the next $5$ minutes. The temperature of the surroundings is:

A monoatomic gas at a pressure $P$, having a volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is: (Take $\gamma = \dfrac{5}{3}$)

A thermodynamic system undergoes the cyclic process $ABCDA$ as shown in the figure. The work done by the system in the cycle is:

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_p$ and $C_v$ respectively. If $\gamma = \dfrac{C_p}{C_v}$ and $R$ is the universal gas constant, then $C_v$ is equal to

A piece of iron is heated in a flame. It first becomes dull red then reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using

A gas is taken through the cycle $A \rightarrow B \rightarrow C \rightarrow A$, as shown. What is the net work done by the gas?

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\dfrac{C_p}{C_v}$ for the gas is

In the given $(V-T)$ diagram, what is the relation between pressures $P_1$ and $P_2$?

An ideal gas goes from state A to state B via three different processes as indicated in the P-V diagram. If $Q_1, Q_2, Q_3$ indicate the heat absorbed by the gas along the three processes and $\Delta U_1, \Delta U_2, \Delta U_3$ indicate the change in internal energy along the three processes respectively, then:

A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27°C to 927°C. The pressure of the gas in its final state is:

The thermo e.m.f. E in volts of a certain thermocouple is found to vary with temperature difference θ in °C between the two junctions according to the relation: $$E = 30\theta - \frac{\theta^2}{15}$$ The neutral temperature for the thermo-couple will be:

A monoatomic gas at pressure P₁ and volume V₁ is compressed adiabatically to 1/8th of its original volume. What is the final pressure of the gas?

Three moles of an ideal gas expanded spontaneously into vacuum. The work done will be:

In thermodynamic processes, which of the following statements is not true?

The internal energy change in a system that has absorbed $2\,\mathrm{kcal}$ of heat and done $500\,\mathrm{J}$ of work is:

If Q, E and W denote respectively the heat added, change in internal energy and the work done in a closed cyclic process, then

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39°W and 239°W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39°C on the Celsius scale?

An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from temperature 20°C? The temperature of boiling water is 100°C.

Can water be boiled without heating?

For a monoatomic ideal gas, the ratio of specific heats γ is equal to:

A Carnot engine whose sink is at 300 K has an efficiency of 40%. By how much should the temperature of source be increased so as to increase its efficiency by 50% of original efficiency?

Which of the following processes is reversible?

The temperature of inversion of a thermocouple is 620°C and the neutral temperature is 300°C. What is the temperature of cold junction?

An ideal gas heat engine operates in Carnot cycle between 227°C and 127°C. It absorbs 6 × 10⁴ cal of heat at higher temperature. Amount of heat converted to work is: