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Q. No.An ideal gas in a thermally insulated vessel at internal pressure = \(P_1,\) volume = \(V_1,\) and absolute temperature = \(T_1\) expands irreversibly 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, which of the following relation(s) hold true?
(a) \(q=0 \)
(b) \( T_2=T_1 \)
(c) \( P_2 V_2=P_1 V_1\)
(d) \(P_2 V_2^\gamma=P_1 V_1^\gamma \)
1. (a), (b), (c)
2. (b), (d)
3, (a), (d)
4. None of the above
(a) \(q=0 \)(b) \( T_2=T_1 \)
(c) \( P_2 V_2=P_1 V_1\)
(d) \(P_2 V_2^\gamma=P_1 V_1^\gamma \)
1. (a), (b), (c)
2. (b), (d)
3, (a), (d)
4. None of the above
Subtopic: Thermodynamics' Properties and process |
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Consider the two given statements:
| Assertion (A): | Heat and work are "definite quantities". |
| Reason (R): | Heat and work are not properties of a system their values depend on the path of the process and vary accordingly. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Thermodynamics' Properties and process |
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At a pressure of \(5 \times 10^5\) bar, the densities of diamond and graphite are 3 g/cc and 2 g/cc, respectively, at a certain temperature T. Calculate the value of \(\Delta U-\Delta H \mathrm{}\) for the conversion of 1 mole of graphite to 1 mole of diamond at a temperature T.
1. \(100 \mathrm{~kJ} / \mathrm{mol}\)
2. \(50 \mathrm{~kJ} / \mathrm{mol}\)
3. \(-~100 \mathrm{~kJ} / \mathrm{mol}\)
4. \(-~50 \mathrm{~kJ} / \mathrm{mol}\)
1. \(100 \mathrm{~kJ} / \mathrm{mol}\)
2. \(50 \mathrm{~kJ} / \mathrm{mol}\)
3. \(-~100 \mathrm{~kJ} / \mathrm{mol}\)
4. \(-~50 \mathrm{~kJ} / \mathrm{mol}\)
Subtopic: Enthalpy & Internal energy |
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Based on the reactions, ascertain the valid algebraic relationship:
| 1. | x = y | 2. | x = 2y |
| 3. | x > y | 4. | x < y |
Subtopic: Enthalpy & Internal energy |
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| Assertion (A): | The heat absorbed during the isothermal expansion of an ideal gas against a vacuum is zero. |
| Reason (R): | The volume occupied by the molecules of an ideal gas is zero. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Enthalpy & Internal energy |
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An ideal gas is expanded irreversibly against 10 bar pressure from 20 litres to 30 litres. Calculate 'w' if the process is isoenthalpic.
| 1. | 0 | 2. | +100J |
| 3. | -100 J | 4. | -10 kJ |
Subtopic: First Law of Thermodynamics |
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A gas is allowed to expand in a well-insulated container against a constant external pressure of 2.5atm from an initial volume of 2.50 L to a final volume of 4.50L. The change in internal energy U of the gas in joules will be:
| 1. | –500J | 2. | –505J |
| 3. | –506J | 4. | –508J |
Subtopic: First Law of Thermodynamics |
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Maximum work is obtained by the system in:
| 1. | Irreversible process | 2. | Reversible process |
| 3. | Adiabatic process | 4. | Isobaric process |
Subtopic: First Law of Thermodynamics |
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Select the correct option based on statements below:
| Statement I: | Total enthalpy change of a multistep process is the sum of ∆H1 + ∆H2 + ∆H3 + . . . |
| Statement II: | When heat is absorbed by the system, the sign of q is taken to be negative. |
| 1. | Statement I is correct; Statement II is correct. |
| 2. | Statement I is correct; Statement II is incorrect. |
| 3. | Statement I is incorrect; Statement II is correct. |
| 4. | Statement I is incorrect; Statement II is incorrect. |
Subtopic: First Law of Thermodynamics |
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Calculate the standard enthalpy of formation (\(\Delta_fH^\circ\)) for 2 moles of liquid benzene (\(\mathrm{{C_6H_6}_{(l)}}\)) at 25°C, based on the given thermodynamic data.
Given Data:
\(\Delta _c\mathrm H\mathrm{(C_6H_6}_\mathrm{(l)})~= -3264.6~ \mathrm{~kJ} / \mathrm{mol}\)
\(\Delta _c\mathrm H\mathrm{(C}_\mathrm{(s)})~= -393.5~ \mathrm{~kJ} / \mathrm{mol}\)
\(\Delta _f\mathrm H\mathrm{(H_2O}_\mathrm{(l)})~= -285.83~ \mathrm{~kJ} / \mathrm{mol}\)
1. \(-~92.22 \mathrm{~kJ} / \mathrm{mol}\)
2. \(-46.11 \mathrm{~kJ} / \mathrm{mol}\)
3. \(+~92.22 \mathrm{~kJ} / \mathrm{mol}\)
4. \(+46.11 \mathrm{~kJ} / \mathrm{mol}\)
Given Data:
\(\Delta _c\mathrm H\mathrm{(C_6H_6}_\mathrm{(l)})~= -3264.6~ \mathrm{~kJ} / \mathrm{mol}\)
\(\Delta _c\mathrm H\mathrm{(C}_\mathrm{(s)})~= -393.5~ \mathrm{~kJ} / \mathrm{mol}\)
\(\Delta _f\mathrm H\mathrm{(H_2O}_\mathrm{(l)})~= -285.83~ \mathrm{~kJ} / \mathrm{mol}\)
1. \(-~92.22 \mathrm{~kJ} / \mathrm{mol}\)
2. \(-46.11 \mathrm{~kJ} / \mathrm{mol}\)
3. \(+~92.22 \mathrm{~kJ} / \mathrm{mol}\)
4. \(+46.11 \mathrm{~kJ} / \mathrm{mol}\)
Subtopic: Thermochemistry |
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