Question

Three different processes that can occur in an ideal monoatomic gas are shown in the $P$ vs $V$ diagram. The paths are labelled as $A\to B,A\to C$ and $A\to D$. The change in internal energies during these process are taken as $E_{AB},E_{AC}$ and $E_{AD}$ and the work done as $W_{AB},W_{AC}$ and $W_{AD}$. The correct relation between these parameters are:

JEE Main 2020 (05 Sep Shift 1)

Options

• A: $E_{\mathit{A}\mathit{B}}=E_{\mathit{A}\mathit{C}}<E_{\mathit{A}\mathit{D}},W_{\mathit{A}\mathit{B}}>0,W_{\mathit{A}\mathit{C}}=0,W_{\mathit{A}\mathit{D}}<0$
• B: $E_{AB}=E_{AC}=E_{AD},W_{AB}>0,W_{AC}=0,W_{AD}<0$
• C: $E_{\mathit{A}\mathit{B}}<E_{\mathit{A}\mathit{C}}<E_{\mathit{A}\mathit{D}},W_{\mathit{A}\mathit{B}}>0,W_{\mathit{A}\mathit{C}}>W_{\mathit{A}\mathit{D}}$
• D: $E_{\mathit{A}\mathit{B}}>E_{\mathit{A}\mathit{C}}>E_{\mathit{A}\mathit{D}},W_{\mathit{A}\mathit{B}}<W_{\mathit{A}\mathit{C}}<W_{\mathit{A}\mathit{D}}$

Question

A thermodynamic cycle $xyzx$ is shown on a $V$ - $T$ diagram.

The $P$ - $V$ diagram that best describes this cycle is: (Diagrams are schematic and not to scale)

JEE Main 2020 (08 Jan Shift 1)

Options

• A:
• B:
• C:
• D:

Question

Starting at temperature $300K,$ one mole of an ideal diatomic gas $\left(\gamma =1.4\right)$ is first compressed adiabatically from volume $V_1$ to $V_2=\frac{V_1}{16}.$ It is then allowed to expand isobarically to volume $2V_2$ . If all the processes are the quasi-static then the final temperature of the gas (in ${}^{o}K$ ) is (to the nearest integer) ___________.

JEE Main 2020 (09 Jan Shift 2)

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Question

Which one is the correct option for the two different thermodynamic processes ?

JEE Main 2021 (17 Mar Shift 2)

Options

• A: (c) and (a)
• B: (c) and (d)
• C: (a) only
• D: (b) and (c)

Question

Which of the following graphs represent the behaviour of an ideal gas? Symbols have their usual meaning.

JEE Main 2021 (20 Jul Shift 2)

Options

• A:
• B:
• C:
• D:

Question

If one mole of an ideal gas at $\left(P_1,V_1\right)$ is allowed to expand reversibly and isothermally ($A$ to $B$) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $\left(B\to C\right).$ Then it is restored to its initial state by a reversible adiabatic compression ($C$ to $A$). The net workdone by the gas is equal to:

JEE Main 2021 (24 Feb Shift 2)

Options

• A: $0$
• B: $RT\ln \left(2\right)$
• C: $-\frac{RT}{2\left(\gamma -1\right)}$
• D: $\mathit{RT}\left[\ln \left(2\right)-\frac{1}{2\left(\gamma -1\right)}\right]$

Question

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27°\mathrm{C}$ to $37°\mathrm{C}$. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? $\left[\mathrm{R}=8.314 \mathrm{J}{ \mathrm{mol}}^{-1}{\mathrm{k}}^{-1}\right]$

JEE Main 2021 (27 Jul Shift 2)

Options

• A: work done by the gas is close to $332 \mathrm{J}$
• B: work done on the gas is close to $582 \mathrm{J}$
• C: work done by the gas is close to $582 \mathrm{J}$
• D: work done on the gas is close to $332 \mathrm{J}$

Question

One mole of an ideal gas at $27 °\mathrm{C}$ is taken from $A$ to $B$ as shown in the given $PV$ indicator diagram. The work done by the system will be _______ $\times {10}^{-1} \mathrm{J}.$ [Given, $R=8.3 \mathrm{J} {\mathrm{mole}}^{-1} \mathrm{K}, \ln 2=0.6931$] (Round off to the nearest integer)

(Round off to the nearest integer)

JEE Main 2021 (20 Jul Shift 2)

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Question

A certain amount of gas of volume $V$ at $27°\mathrm{C}$ temperature and pressure $2\times {10}^7\mathrm{N} {\mathrm{m}}^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma =1.5$)

JEE Main 2022 (25 Jul Shift 1)

Options

• A: $3.536\times {10}^5 \mathrm{Pa}$
• B: $3.536\times {10}^6 \mathrm{Pa}$
• C: $1.25\times {10}^6 \mathrm{Pa}$
• D: $1.25\times {10}^5 \mathrm{Pa}$

Question

At a certain temperature, the degrees of freedom per molecule for gas is $8$. The gas performs $150 \mathrm{J}$ of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _____ $\mathrm{J}$.

JEE Main 2022 (28 Jul Shift 2)

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Question

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $T_3>T_2>T_1$ as:

JEE Main 2023 (24 Jan Shift 2)

Options

• A:
• B:
• C:
• D:

Question

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:

JEE Main 2023 (24 Jan Shift 2)

Options

• A: $\frac{27}{35}$
• B: $\frac{35}{27}$
• C: $\frac{25}{21}$
• D: $\frac{21}{25}$

Question

A hypothetical gas expands adiabatically such that its volume changes from $08$ litres to $27$ litres. If the ratio of final pressure of the gas to initial pressure of the gas is$\frac{16}{81}$ . Then the ratio of $\frac{C_p}{C_v}$ will be.

JEE Main 2023 (31 Jan Shift 2)

Options

• A: $\frac{4}{3}$
• B: $\frac{3}{1}$
• C: $\frac{1}{2}$
• D: $\frac{3}{2}$

Question

P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct :

JEE Main 2024 (04 Apr Shift 1)

Options

• A: $\rho_1>\rho_2$
• B: $\rho_2 < \rho_3$
• C: $\rho_1=\rho_2=\rho_3$
• D: $\rho_1 < \rho_2$

Question

A sample of 1 mole gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma=\frac{3}{2}$, then the work done by the gas in the process is:

JEE Main 2024 (09 Apr Shift 1)

Options

• A: $\frac{R}{T}[2-\sqrt{2}]$
• B: $\frac{T}{R}[2+\sqrt{2}]$
• C: RT $[2-\sqrt{2}]$
• D: $\mathrm{RT}[2+\sqrt{2}]$

Question

A real gas within a closed chamber at $27^{\circ} \mathrm{C}$ undergoes the cyclic process as shown in figure. The gas obeys $P V^3=R T$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R=8 \mathrm{~J} / \mathrm{mol} \mathrm{K}$ ):

JEE Main 2024 (09 Apr Shift 2)

Options

• A: $20 \mathrm{~J}$
• B: $205 \mathrm{~J}$
• C: $-20 \mathrm{~J}$
• D: $225 \mathrm{~J}$

Question

A thermodynamic system is taken from an original state $A$ to an intermediate state $B$ by a linear process as shown in the figure. Its volume is then reduced to the original value from $B$ to $C$ by an isobaric process. The total work done by the gas from $A$ to $B$ and $B$ to $C$ would be :

JEE Main 2024 (29 Jan Shift 1)

Options

• A: $33800 \mathrm{J}$
• B: $2200 \mathrm{J}$
• C: $600 \mathrm{J}$
• D: $800 \mathrm{J}$

Question

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

JEE Main 2024 (27 Jan Shift 2)

Options

• A: $\frac{5}{3}$
• B: $\frac{3}{2}$
• C: $\frac{7}{5}$
• D: $\frac{9}{7}$

Question

The given figure represents two isobaric processes for the same mass of an ideal gas, then

JEE Main 2024 (31 Jan Shift 1)

Options

• A: $P_2\ge P_1$
• B: $P_2>P_1$
• C: $P_1=P_2$
• D: $P_1>P_2$