Final answer:
The change in internal energy can be calculated using the first law of thermodynamics, with the given heat absorbed and the work done during gas expansion. After converting the provided values to consistent units, we apply the formula ΔU = Q - W to find the answer.
Step-by-step explanation:
To calculate the change in internal energy for a system absorbing heat and performing work through expansion, we use the first law of thermodynamics, which is ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Given that the system absorbs 93.7 kJ of heat (Q) and is expanding against a constant pressure, we need to find the work done. Work (W) can be found using the equation W = PΔV, where P is the pressure and ΔV is the change in volume. The volume change (ΔV) is from 8.00 L to 24.00 L, which equals 16.00 L. The pressure P is given in atm, but we need to convert it to the SI unit Pascal (Pa) or we can convert the volume from liters to cubic meters and use the pressure in atm. Using either method, work can be calculated and then converted to joules if necessary. After calculating W, we can find ΔU by substracting W from Q.