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.

Which of the following relation(s) are correct for this expansion?

(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) and (c)
2. (b) and (d)
3. (a) and (d)
4. None of the above
Subtopic: Ā Thermodynamics' Properties and process |
Level 3: 35%-60%
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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: Ā Thermodynamics' Properties and process |
Level 3: 35%-60%
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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. 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 is:

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: Ā Thermodynamics' Properties and process |Ā Thermochemistry |
Level 3: 35%-60%
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