4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20 L. — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

**Step 1: Identify the process type** Free expansion into vacuum is an irreversible, adiabatic process where the gas expands without doing work against external pressure. **Step 2: Determine work done** In free expansion into vacuum, the external pressure is zero (P_ext = 0). Using W = -P_ext·ΔV: W = -0 × ΔV = 0 L·atm **Step 3: Apply the First Law of Thermodynamics** ΔU = q + w where ΔU is change in internal energy, q is heat absorbed, and w is work done by the gas. **Step 4: Determine change in internal energy** For an ideal gas expanding isothermally, temperature remains constant. Since U depends only on temperature for an ideal gas: ΔU = 0 **Step 5: Calculate heat absorbed** 0 = q + 0 q = 0 L·atm **Step 6: Interpret the result** In free expansion, no work is done and internal energy doesn't change, so no heat is exchanged with surroundings. Therefore, the answer is 0.00.