Import Question JSON

$\text{Hint: Isenthalpic means } \Delta H = \text{zero}$ $\text{Step 1: Understand what an isenthalpic process means}$ $\text{An isenthalpic process is one in which the enthalpy remains constant, i.e., } \Delta H = 0.$ $\text{Step 2: Calculate the work done during the expansion}$ $\text{For an irreversible expansion against a constant external pressure, the work is given by:}$ $W = -P_{\text{ext}}\Delta V$ $\text{Where:}$ $P_{\text{ext}} = \text{external pressure} = 10 \text{ bar}$ $\Delta V = V_2 - V_1 = \text{change in volume} = 30 - 20 = 10 \text{ litres}$ $W = -P_{\text{ext}}\Delta V = -10 \text{ bar} \times 10 \text{ L} = -100 \text{ bar L}$ $\text{Step 3: Convert the units to joules}$ $\text{To convert from bar L to joules, we use the conversion factor:}$ $1 \text{ bar L} = \frac{8.314 \text{ J mol}^{-1}\text{ K}^{-1}}{0.0824 \text{ L bar mol}^{-1}\text{ K}^{-1}} = 100 \text{ J}$ $\text{Therefore:}$ $W = -100 \text{ bar L} \times 100 \text{ J/bar L} = -10,000 \text{ J} = -10 \text{ kJ}$ $\text{Step 4: Verify the answer using the first law of thermodynamics}$ $\text{The first law of thermodynamics states that:}$ $\Delta U = q + W$ $\text{For an isenthalpic process, } \Delta H = 0$ $\text{Recall that } \Delta H = \Delta U + \Delta(PV)$ $\text{For an ideal gas, } \Delta(PV) = \Delta(nRT) \text{, which is zero for a constant temperature process.}$ $\text{Therefore, for an isenthalpic process of an ideal gas, } \Delta U = 0 \text{ as well.}$ $\text{From the first law, if } \Delta U = 0\text{, then } q = -W$ $\text{This confirms that heat is transferred into the system (positive q) to balance the negative work done by the system.}$ $\text{The work done is } W = -10 \text{ kJ} \text{, which corresponds to option 4.}$