Thermodynamics Questions | JEE Main Chemistry Chapter Wise Question Papers

Q 1 :
Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following: [2024]

$q = 0, Δ T \neq 0, w = 0$
$q = 0, Δ T < 0, w \neq 0$
$q \neq 0, Δ T = 0, w = 0$
$q = 0, Δ T = 0, w = 0$

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(D) For adiabatic process $q = 0$ .

$W = - P_{ext} Δ V, for free expansion, P_{ext} = 0, so w = 0$

By first law of thermodynamics:

$Δ U = W + q$

$Δ U = 0 + 0 = 0$

For an ideal gas internal energy is function of temperature, so if $Δ U = 0, Δ T$ is also 0.

Q 2 :
If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible condition then work, w, is $- x$ J. The value of $x$ is _________ .

(Given R = 8.314 J $K^{- 1}$ $m o l^{- 1}$ ) [2024]

0%

(28721)

For isothermal reversible process, work W is given by:

$W = - 2.303$ $n R T$ $\log$ $\frac{V_{2}}{V_{1}}$

$= - 2.303 \times 5$ $mol \times 8.314 \frac{J}{mol K} \times 300$ $K$ $l o g$ $\frac{100}{10}$

$= - 28720.713$ $J \approx - 28721 J$

Q 3 :
The heat of combustion of solid benzoic acid at constant volume is –321.30 kJ at 27°C. The heat of combustion at constant pressure is (–321.30 – $x$ R) kJ, the value of $x$ is _________ . [2024]

0%

(150)

$C_{6} H_{5} COOH (s) + \frac{15}{2} O_{2} (g) \to 7 {CO}_{2} (g) + 3 H_{2} O (l)$

$Δ n_{g} = Gaseous moles of products - Gaseous moles of reactants$

$= 7 - 7.5 = - 0.5$

$Heat of combustion at constant pressure (Δ H) is related to heat of combustion at constant volume (Δ U) by :$

$Δ H = Δ U + Δ n_{g} R T$

$Δ H = - 321.3 - 0.5 R \times 300$

$Δ H = - 321.3 - 150 R$

Q 4 :
$Δ_{vap} H^{Θ}$ for water is + 40.79 kJ $m o l^{- 1}$ at 1 bar and 100°C. Change in internal energy for this vapourisation under same condition is ________ kJ $m o l^{- 1}$ . (Integer answer)

(Given R = 8.3 $J K^{- 1}$ $m o l^{- 1}$ ) [2024]

0%

(38)

$H_{2} O (l) ⇌ H_{2} O (g)$

$Δ n_{g} = Gaseous moles of products - Gaseous moles of reactants$

$= 1 - 0 = 1$

$Δ H = Δ U + Δ n_{g} R T$

$40.79 {kJmol}^{- 1} = Δ U + 1 \times 8.3 \frac{J}{molK} \times 373 K$

$40.79 {kJmol}^{- 1} = Δ U + 1 \times \frac{8.3}{1000} \frac{kJ}{molK} \times 373 K$

$Δ U = 37.69 {kJmol}^{- 1} \approx 38 {kJmol}^{- 1}$

Q 5 :
If three moles of an ideal gas at 300 K expand isothermally from 30 ${dm}^{3}$ to 45 ${dm}^{3}$ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is _____ J. [2024]

0%

(1200)

[IMAGE 8]

Work (W) against constant pressure is calculated as:

$W = - P_{ext} (V_{2} - V_{1}) = - 80 kPa \times (45 - 30) {dm}^{3}$

$= - 80 \times 1000 Pa \times 15 \times {(10^{- 1} m)}^{3}$

$= - 1200 J$

By first law of thermodynamics:

$Δ U = Q + W$

For isothermal process of an ideal gas, $Δ U = 0$

So, $Q = - W$

$Q = - (- 1200 J) = 1200 J$

Hence 1200 J of heat is absorbed in the process.

Q 6 :
[IMAGE 9]

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path $A \to B \to C \to A$ as shown in the diagram above. The total work done in the process is _____ J. [2024]

0%

(200)

Magnitude of work done in a cyclic process = area enclosed by P-V or V-P graph.

$| W |$ $= \frac{1}{2} \times A C \times A B$

$= \frac{1}{2} \times (30 - 10) kPa \times (30 - 10) {dm}^{3}$

$= 200 {kPadm}^{3}$

$= 200 \times 1000 Pa \times {(10^{- 1} m)}^{3}$

$= 200 {Pam}^{3} = 200 J$

Q 7 :
[IMAGE 10]

Consider the figure provided.

1 mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at 18°C. If the piston is moved to position B, keeping the temperature unchanged, then ‘x’ L atm work is done in this reversible process.

x = _____ L atm. (nearest integer)

[Given: Absolute temperature = °C + 273.15,
R = 0.08206 L atm ${mol}^{- 1}$ $K^{- 1}$ ] [2024]

0%

(55)

Work done by gas in isothermal reversible expansion is:

$w = - 2.303 n R T \log_{10} \frac{V_{2}}{V_{1}}$

$w = - 2.303 \times 1 \times 0.08206 \times 291.15 \times \log_{10} \frac{100}{10} atmL$

$w = - 2.303 \times 1 \times 0.08206 \times 291.15 \times \log_{10} 10 atmL$

$w = - 55.023 atmL \approx - 55 atmL$

Work done by system = +55 atmL

Topic Question Set

Q 1 :
Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following: [2024]

Q 2 :
If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible condition then work, w, is $- x$ J. The value of $x$ is _________ .

(Given R = 8.314 J $K^{- 1}$ $m o l^{- 1}$ ) [2024]

0%

Q 3 :
The heat of combustion of solid benzoic acid at constant volume is –321.30 kJ at 27°C. The heat of combustion at constant pressure is (–321.30 – $x$ R) kJ, the value of $x$ is _________ . [2024]

0%

Q 4 :
$Δ_{vap} H^{Θ}$ for water is + 40.79 kJ $m o l^{- 1}$ at 1 bar and 100°C. Change in internal energy for this vapourisation under same condition is ________ kJ $m o l^{- 1}$ . (Integer answer)

(Given R = 8.3 $J K^{- 1}$ $m o l^{- 1}$ ) [2024]

0%

Q 5 :
If three moles of an ideal gas at 300 K expand isothermally from 30 ${dm}^{3}$ to 45 ${dm}^{3}$ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is _____ J. [2024]

0%

Q 6 :
[IMAGE 9]

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path $A \to B \to C \to A$ as shown in the diagram above. The total work done in the process is _____ J. [2024]

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0%

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Topic Question Set

Q 1 : Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following: [2024]

Q 2 : If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible condition then work, w, is -x J. The value of x is _________ . (Given R = 8.314 J K-1 mol-1) [2024]

0%

Q 3 : The heat of combustion of solid benzoic acid at constant volume is –321.30 kJ at 27°C. The heat of combustion at constant pressure is (–321.30 – xR) kJ, the value of x is _________ . [2024]

0%

Q 4 : ΔvapHΘ for water is + 40.79 kJ mol-1 at 1 bar and 100°C. Change in internal energy for this vapourisation under same condition is ________ kJ mol-1. (Integer answer) (Given R = 8.3 JK-1 mol-1) [2024]

0%

Q 5 : If three moles of an ideal gas at 300 K expand isothermally from 30 dm3 to 45 dm3 against a constant opposing pressure of 80 kPa, then the amount of heat transferred is _____ J. [2024]

0%

Q 6 : [IMAGE 9] An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A→B→C→A as shown in the diagram above. The total work done in the process is _____ J. [2024]

0%

0%

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Q 1 :
Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following: [2024]

Q 2 :
If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible condition then work, w, is $- x$ J. The value of $x$ is _________ .

(Given R = 8.314 J $K^{- 1}$ $m o l^{- 1}$ ) [2024]

Q 3 :
The heat of combustion of solid benzoic acid at constant volume is –321.30 kJ at 27°C. The heat of combustion at constant pressure is (–321.30 – $x$ R) kJ, the value of $x$ is _________ . [2024]

Q 4 :
$Δ_{vap} H^{Θ}$ for water is + 40.79 kJ $m o l^{- 1}$ at 1 bar and 100°C. Change in internal energy for this vapourisation under same condition is ________ kJ $m o l^{- 1}$ . (Integer answer)

(Given R = 8.3 $J K^{- 1}$ $m o l^{- 1}$ ) [2024]

Q 5 :
If three moles of an ideal gas at 300 K expand isothermally from 30 ${dm}^{3}$ to 45 ${dm}^{3}$ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is _____ J. [2024]

Q 6 :
[IMAGE 9]

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path $A \to B \to C \to A$ as shown in the diagram above. The total work done in the process is _____ J. [2024]