Heat and Thermodynamics

Ten moles of an ideal monoatomic gas, initially in state $\boldsymbol{a}$ at atmospheric pressure and temperature $T_a=27^{\circ} \mathrm{C}$, is enclosed in a metal cylinder of volume $V_0$ fitted with a frictionless piston. The gas is sud...

As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition ($P_1$) and a freely movable but thermally insulated piston ($P_2$). The partition $P_1$ with thermal conductivity $K$, cross secti...

As shown in the figure, five Carnot engines, each with efficiency $\eta$ and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the n...

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process $(ab)$, followed by an isochoric process $(bc)$ and an adiabatic process $(ca)$ as shown in the figure. The volumes of the gas are $V_1$ and $V_2$ at $a$ and $b$,...

The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, ...

An ideal monatomic gas of $n$ moles is taken through a cycle $W X Y Z W$ consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic $V-T$ diagram. The volume of the gas at $W, X$ and $Y$ points are, $...

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4 . It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump...

Two identical plates P and Q , radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $\mathrm{T}_{\mathrm{P}}$ and $\mathrm{T}_{\mathrm{Q}}$, respectively, with $\mathrm{T}_{\mathrm{Q}}<\mathrm{T}_{\mathrm{...

A spherical soap bubble inside an air chamber at pressure $P_0=10^5 \mathrm{~Pa}$ has a certain radius so that the excess pressure inside the bubble is $\Delta P=144 \mathrm{~Pa}$. Now, the chamber pressure is reduced to $8 P_0 / 27$ so tha...

One mole of a monatomic ideal gas undergoes the cyclic process $\mathrm{J} \rightarrow \mathrm{K} \rightarrow \mathrm{L} \rightarrow \mathrm{M} \rightarrow \mathrm{J}$, as shown in the P-T diagram.



Match the quantities mentioned in List-...

The specific heat capacity of a substance is temperature dependent and is given by the formula $C=k T$, where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the tempe...

When the chimney is closed using a cap at the top, a pressure difference $\Delta P$ develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, ...

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _________ $\mathrm{gm} \mathrm{s}^{-1}$.

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P-V$ diagrams below. In cycle I, processes $a, b, c$ and $d$ are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes...

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $\mathrm{v}_n$. At a fixed temperature ...

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.
[Given: Wien's constant as $2.9 \times 10^{-3} \mathrm{~m}-\mathrm{K}$ and $\frac{h c}{e}=1.24 \times 10^{-6} \ma...

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma=5 / 3)$ and one mole of an ideal diatomic gas $(\gamma=7 / 5)$. Here, $\gamma$ is the ratio of the specific heats at constant pressure and con...

One mole of an ideal gas expands adiabatically from an initial state $\left(T_{\mathrm{A}}, V_0\right)$ to final state $\left(T_{\mathrm{f}}, 5 V_0\right)$. Another mole of the same gas expands isothermally from a different initial state $\...

In the given $P-V$ diagram, a monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} ...

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

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The value of \({Q \over {R{T_0}}}\) is

The value of \({{{T_R}} \over {{T_0}}}\) is

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/c...

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/c...

A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t ...

An ideal gas undergoes a four step cycle as shown in the P-V diagram below. During this cycle, heat is absorbed by the gas in

A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R \(-\) a). For a << R the magnitu...

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm\(-\)2 and it is absorbed by the wate...

A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two
equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the
partition is held initially at a...

The filament of a light bulb has surface area 64 mm2
. The filament can be considered as a black
body at temperature 2500 K emitting radiation like a point source when viewed from far. At night
the light bulb is observed from a distance of ...

Consider one mole of helium gas enclosed in a container at initial pressure P1 and volume V1. It
expands isothermally to volume 4V1. After this, the gas expands adiabatically and its volume becomes
32V1. The work done by the gas during isot...

If the process carried out on one mole of monoatomic ideal gas is as shown in the PV-diagram with \({p_0}{V_0} = {1 \over 3}R{T_0}\), the correct match is,

If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with \({P_0}{V_0} = {1 \over 3}R{T_0}\), the correct match is,

A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P0, volume V0, and temperature T0. If the gas mixture is adiabatically compressed to a volume \({{{V_0}} \over 4}\), then t...

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are [R is the gas constant]

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the \(PV\)-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the pr...

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is \(100\,K\) and the universal gas constant \(R=8.0\) $$J\,mo{l^{ - 1}}{K^{...

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where \(V\) is the volume and \(T\) is the temperature). Which of the statements below is (are) true?

Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

Which of the following options is the only correct representation of a process in which
\(\Delta U = \Delta Q - P\Delta V\)?

Which one of the following options is the correct combination?

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at
pressure Pi = 105 Pa and volume Vi = 10-3 m3 changes to a final state at Pf = \(\left( {{1 \over {32}}} \right) \times {10^5}\,Pa\) and
V...

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires
has a length of 1 m at 10oC. Now the end P is maintained at 10oC, while the end S is heated and
maintained at 400oC. The system is th...

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P)
by the metal. The sensor has a scale that displays \({\log _2}\left( {{P \over {{P_0}}}} \right)\), where P0 is a constant. When th...

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that genera...

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. The gas is then heate...

Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits
104 times the power emitted from B. The ratio \(\left( {{{{\lambda _A}} \over {{\lambda _B}}}} \right)\) of their wavelengths $${{\lamb...

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium
at temperature T. Assuming the gases are ideal, the correct statement(s) is(are)

Parallel rays of light of intensity \(I\) = 912 Wm–2 are incident on a spherical black body kept in surroundings
of temperature 300 K. Take Stefan-Boltzmann constant \(\sigma\) = 5.7 \(\times\) 10–8 Wm–2K–4 and assume that the energy
exc...

Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be