Calculate the change in internal energy (AU) for a system that is giving off 24.0 kJ of heat and is changing from 22..00 L to 19.00 L in volume at 1.50 atm pressure. (Remember that 101.3J=1Lcdot atm) -23.5kJ +24.5 kJ 444 kJ -24.5kJ -16.0kJ

Here's how to calculate the change in internal energy:<br /><br />**Understanding the Concepts**<br /><br />* **First Law of Thermodynamics:** The change in internal energy (ΔU) of a system is equal to the heat added to the system (q) minus the work done by the system (w). ΔU = q - w<br /><br />* **Work and Volume Change:** Work done by a system against a constant external pressure is given by: w = PΔV, where P is the pressure and ΔV is the change in volume.<br /><br />**Calculations**<br /><br />1. **Calculate the work (w):**<br /> * ΔV = V_final - V_initial = 19.00 L - 22.00 L = -3.00 L (Volume decreased)<br /> * w = (1.50 atm)(-3.00 L) = -4.50 L·atm<br /><br />2. **Convert work to joules:**<br /> * w = (-4.50 L·atm) * (101.3 J / 1 L·atm) = -455.85 J = -0.45585 kJ (rounded to -0.46 kJ for simplicity in the next step)<br /><br />3. **Calculate the change in internal energy (ΔU):**<br /> * q = -24.0 kJ (Heat is given off, so it's negative)<br /> * ΔU = q - w = -24.0 kJ - (-0.46 kJ) = -24.0 kJ + 0.46 kJ = -23.54 kJ<br /><br />4. **Round to significant figures:** The least number of decimal places in the given values is one (in 1.50 atm). Therefore, the final answer should also have one decimal place.<br /><br />**Final Answer:**<br /><br />ΔU = -23.5 kJ (This matches the first option provided)<br />