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