First Law of Thermodynamics

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JEE Advanced 2026

An ideal gas ( $0.5 mol$ ), initially at $2 bar$ pressure, is compressed at a constant temperature of $600 K$ in two steps : first against a constant external pressure of $P bar$ ( $2 < P < 8$ ), and then against constant external pressure of $8 bar$ . At each step, the compression is stopped only when the pressure of the gas becomes equal to the external pressure. The total work done on the gas in these steps is $W$ . Considering all possible values of $P$ ( $2 < P < 8$ ) and taking the gas constant as $R$ (in $J K^{- 1} mol^{- 1}$ ), the minimum value of $∣ W ∣$ (in $J$ ) is

207 R

(B)

600 R

(C)

630 R

(D)

900 R

JEE Advanced 2025

LEVELJEE Main

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is _______. Use: Universal gas constant (R) = 8.3 J K $^{- 1}$ mol $^{- 1}$ ; Atomic mass (in amu): H = 1, O = 16

JEE Advanced 2017

LEVELJEE Advanced

An ideal gas is expanded from $(p_{1}, V_{1}, T_{1})$ to $(p_{2}, V_{2}, T_{2})$ under different conditions. The correct statement(s) among the following is(are)

* Multiple Correct Options

(A)

The work done on the gas is maximum when it is compressed irreversibly from

(p_{2}, V_{2})

(p_{1}, V_{1})

against constant pressure

p_{1}

(B)

The work done on the gas is less when it is expanded reversibly from

V_{1}

V_{2}

under adiabatic conditions as compared to that when expanded reversibly from

V_{1}

V_{2}

under isothermal conditions.

(C)

The change in internal energy of the gas (i) zero, if it is expanded reversibly with

T_{1} = T_{2}

, and (ii) positive, if it is expanded reversibly under adiabatic conditions with

T_{1} \neq = T_{2}

(D)

If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic.

JEE Advanced 2018

LEVELJEE Advanced

A reversible cyclic process for an ideal gas is shown below. Here, P , V and T are pressure , volume and temperature , respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.

* Multiple Correct Options

(A)

q_{AC} = Δ U_{BC}

and

w_{AB} = P_{2} (V_{2} - V_{1})

(B)

w_{BC} = P_{2} (V_{2} - V_{1})

and

q_{BC} = Δ H_{AC}

(C)

Δ H_{CA} < Δ U_{CA}

and

q_{AC} = Δ U_{BC}

(D)

q_{BC} = Δ H_{AC}

and

Δ H_{CA} > Δ U_{CA}

JEE Advanced 2021

LEVELJEE Advanced

One mole of an ideal gas at $900 K$ , undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $ln \frac{V _{3}}{V _{2}}$ is ___. ( $U$ : internal energy, $S$ : entropy, $p$ : pressure, $V$ : volume, $R$ : gas constant) (Given: molar heat capacity at constant volume, $C_{V, m}$ of the gas is $\frac{5}{2} R$ )

JEE Advanced 2023

LEVELJEE Advanced

One mole of an ideal monoatomic gas undergoes two reversible processes (A $\to$ B and B $\to$ C) as shown in the given figure : A $\to$ B is an adiabatic process. If the total heat absorbed in the entire process (A $\to$ B and B $\to$ C) is $R T_{2} ln 10$ , the value of $2 lo g V_{3}$ is _________. [Use, molar heat capacity of the gas at constant pressure, $C_{p, m} = \frac{5}{2} R$ ]

JEE Advanced 2022

LEVELJEE Advanced

2 mol of Hg(g) is combusted in a fixed volume bomb calorimeter with excess of O $_{2}$ at 298 K and 1 atm into HgO(s). During the reaction, temperature increases from 298.0 K to 312.8 K. If heat capacity of the bomb calorimeter and enthalpy of formation of Hg(g) are 20.00 kJ K $^{- 1}$ and 61.32 kJ mol $^{- 1}$ at 298 K, respectively, the calculated standard molar enthalpy of formation of HgO(s) at 298 K is X kJ mol $^{- 1}$ . The value of |X| is ______. [Given : Gas constant R = 8.3 J K $^{- 1}$ mol $^{- 1}$ ]

JEE Advanced 2014

LEVELJEE Main

An ideal gas in thermally insulated vessel at internal pressure = $P_{1}$ , volume = $V_{1}$ and absolute temperature = $T_{1}$ expands irrversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are $P_{2}$ , $V_{2}$ and $T_{2}$ , respectively. For this expansion,

* Multiple Correct Options

(A)

q = 0

(B)

T_{2} = T_{1}

(C)

P_{2} V_{2} = P_{1} V_{1}

(D)

P_{2} V_{2}^{γ} = P_{1} V_{1}^{γ}

JEE Advanced 2020

LEVELJEE Main

In thermodynamics the P-V work done is given by $w = - \int d V P_{ext}$ . For a system undergoing a particular process, the work done is, $w = - \int d V (\frac{R T}{V - b} - \frac{a}{V ^{2}})$ . This equation is applicable to a

* Multiple Correct Options

(A)

System that satisfies the van der Waals equation of state.

(B)

Process that is reversible and isothermal.

(C)

Process that is reversible and adiabatic.

(D)

Process that is irreversible and at constant pressure.

JEE Main 2021

LEVELJEE Main

The reaction of cyanamide, $NH_{2} CN (s)$ with oxygen was run in a bomb calorimeter and $Δ U$ was found to be $- 742.24 kJ mol^{- 1}$ . The magnitude of $Δ H_{298}$ for the reaction $NH_{2} CN (s) + \frac{3}{2} O_{2} (g) ⟶ N_{2} (g) + CO_{2} (g) + H_{2} O (l)$ is ......... kJ (Rounded off to the nearest integer). [Assume ideal gases and $R = 8.314 J mol^{- 1} K^{- 1}$ ]

JEE Main 2017

LEVELJEE Main

$Δ U$ is equal to

The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is ……… .

JEE Main 2021

LEVELJEE Main

For water $Δ_{vap} H = 41 kJ mol^{- 1}$ at $373 K$ and $1 bar$ pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water, the internal energy change during evaporation of water is ......... $kJ mol^{- 1}$ . [Use $R = 8.3 J mol^{- 1} K^{- 1}$ ]

LEVELJEE Main

A heat engine absorbs heat $q_{1}$ from a source at temperature $T_{1}$ and heat $q_{2}$ from a source at temperature $T_{2}$ . Work done is found to be $J (q_{1} + q_{2})$ . This is in accordance with

(A)

First law of thermodynamics

(B)

Second law of thermodynamics

(C)

Joules equivalent law

The combustion of benzene ( $l$ ) gives $C O_{2} (g)$ and $H_{2} O (l)$ . Given that heat of combustion of benzene at constant volume is $- 3263.9 kJ mol^{- 1}$ at $2 5^{\circ} C$ ; heat of combustion (in $kJ mol^{- 1}$ ) of benzene at constant pressure will be ( $R = 8.314 J K^{- 1} mol^{- 1}$ )

(A)

4152.6

(B)

- 452.46

(C)

3260

(D)

- 3267.6

JEE Main 2020

LEVELJEE Main

The internal energy change (in J) when $90 g$ of water undergoes complete evaporation at $10 0^{\circ} C$ is ........., (Given : $Δ H_{vap}$ for water at $373 K = 41 kJ/mol$ , $R = 8.314 J K^{- 1} mol^{- 1}$ )

JEE Main 2019

LEVELJEE Main

The difference between $Δ H$ and $Δ U$ ( $Δ H - Δ U$ ), when the combustion of one mole of heptane (l) is carried out at a temperature $T$ , is equal to

(A)

- 4 R T

(B)

3 R T

(C)

4 R T

(D)

- 3 R T

JEE Main 2020

LEVELBoard

At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal energy by 5000 J. The molar heat capacity at constant volume is ............

LEVELBoard

Heat required to raise the temperature of $1 mole$ of a substance by $1^{\circ}$ is called

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temp. $T_{1}$ and $T_{2}$ ( $T_{1} < T_{2}$ ). The correct graphical depiction of the dependence of work done ( $W$ ) on the final volume ( $V$ ) is

Among the following the set of parameters that represents path functions, is (A) $q + W$ (B) $q$ (C) $W$ (D) $H - T S$

For one mole of an ideal gas, which of these statements must be true? (A) $U$ and $H$ each depends only on temperature. (B) Compressibility factor $Z$ is not equal to $1$ . (C) $C_{p, m} - C_{V, m} = R$ (D) $d U = C_{V} d T$ for any process.

An ideal gas expands in volume from $1 im es 1 0^{- 3} m^{3}$ to $1 im es 1 0^{- 2} m^{3}$ at $300 K$ against a constant pressure of $1 im es 1 0^{5} Nm^{- 2}$ . The work done is

(A)

- 900 J

(B)

- 900 kJ

(C)

270 kJ

(D)

900 kJ

JEE Main 2021

LEVELJEE Main

For water at $10 0^{\circ} C$ and $1 bar$ , $Δ_{vap} H - Δ_{vap} U = \dots \times 1 0^{2} J mol^{- 1}$ . (Round off to the nearest integer) [Use : $R = 8.31 J mol^{- 1} K^{- 1}$ ] [Assume volume of $H_{2} O (l)$ is much smaller than volume of $H_{2} O (g)$ . Assume $H_{2} O (g)$ treated as an ideal gas]

JEE Main 2019

LEVELJEE Main

For silver, $C_{p} (J K^{- 1} mol^{- 1}) = 23 + 0.01 T$ . If the temperature ( $T$ ) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of $Δ H$ will be close to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An ideal gas is expanded from (p1​,V1​,T1​) to (p2​,V2​,T2​) under different conditions. The correct statement(s) among the following is(are)

A reversible cyclic process for an ideal gas is shown below. Here, P , V and T are pressure , volume and temperature , respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.

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The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is ……… .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The difference between ΔH and ΔU (ΔH−ΔU), when the combustion of one mole of heptane (l) is carried out at a temperature T, is equal to

At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal energy by 5000 J. The molar heat capacity at constant volume is ............

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Heat required to raise the temperature of 1 mole of a substance by 1∘ is called

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Among the following the set of parameters that represents path functions, is (A) q+W (B) q (C) W (D) H−TS

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An ideal gas expands in volume from 1imes10−3 m3 to 1imes10−2 m3 at 300 K against a constant pressure of 1imes105 Nm−2. The work done is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For silver, Cp​(J K−1mol−1)=23+0.01T. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of ΔH will be close to

An ideal gas is expanded from $(p_{1}, V_{1}, T_{1})$ to $(p_{2}, V_{2}, T_{2})$ under different conditions. The correct statement(s) among the following is(are)

$Δ U$ is equal to

The difference between $Δ H$ and $Δ U$ ( $Δ H - Δ U$ ), when the combustion of one mole of heptane (l) is carried out at a temperature $T$ , is equal to

Heat required to raise the temperature of $1 mole$ of a substance by $1^{\circ}$ is called

Among the following the set of parameters that represents path functions, is (A) $q + W$ (B) $q$ (C) $W$ (D) $H - T S$

An ideal gas expands in volume from $1 im es 1 0^{- 3} m^{3}$ to $1 im es 1 0^{- 2} m^{3}$ at $300 K$ against a constant pressure of $1 im es 1 0^{5} Nm^{- 2}$ . The work done is

For silver, $C_{p} (J K^{- 1} mol^{- 1}) = 23 + 0.01 T$ . If the temperature ( $T$ ) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of $Δ H$ will be close to