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When \( 100 \mathrm{~mL} \) of \( 1.0 \mathrm{M} \mathrm{HCl} \) was mixed with \( 100 \mathrm{~mL} \) of \( 1.0 \mathrm{M} \mathrm{NaOH} \) in an insulated beaker at constant pressure, a temperature increase of \( 5.7^{\circ} \mathrm{C} \) was measured
\( \mathrm{P} \) for the beaker and its contents (Expt. 1). Because the

W enthalpy of neutralization of a strong acid with a strong base is a constant \( \left(-57.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\right) \), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), \( 100 \mathrm{~mL} \) of 2.0 M acetic acid \( \left(\mathrm{K}_{\mathrm{a}}=\right. \) \( 2.0 \times 10^{-5} \) ) was mixed with \( 100 \mathrm{~mL} \) of \( 1.0 \mathrm{M} \mathrm{NaOH} \) (under identical conditions to Expt. 1) where a temperature rise of \( 5.6^{\circ} \mathrm{C} \) was measured.
(Consider heat capacity of all solutions as \( 4.2 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-} \) and density of all solutions as \( 1.0 \mathrm{~g} \mathrm{~mL}^{-1} \) )
An ideal gas in a thermally insulated vessel at internal pressure \( =\mathrm{P}_{1} \), volume \( =\mathrm{V}_{1} \) 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,
[JEE Advanced-2014]
(A) \( q=0 \)
(B) \( \mathrm{T}_{2}=\mathrm{T}_{1} \)
(C) \( \mathrm{P}_{2} V_{2}=P_{1} V_{l} \)
(D) \( P_{2} V_{2}^{\gamma}=P_{1} V_{1}^{\gamma} \)
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