A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of the change — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

**Step 1: Identify the First Law of Thermodynamics** The relationship between internal energy, heat, and work is: $$\Delta U = q - w$$ where: - ΔU = change in internal energy - q = heat absorbed by the system - w = work done by the system **Step 2: Identify the given values** - Work done by the system: w = 200 J - Heat absorbed by the system: q = 150 J **Step 3: Apply the sign convention** Since the system does work on surroundings, w is positive (200 J). Since the system absorbs heat, q is positive (150 J). **Step 4: Substitute into the formula** $$\Delta U = q - w$$ $$\Delta U = 150 \text{ J} - 200 \text{ J}$$ **Step 5: Calculate the change in internal energy** $$\Delta U = -50 \text{ J}$$ **Step 6: Find the magnitude** The magnitude of the change in internal energy is the absolute value: $$|\Delta U| = |-50| = 50 \text{ J}$$ Therefore, the answer is 50.00.