Calculate the change in internal energy (Delta U) for a system that is giving off 50.0 kJ of heat and is performing 855 J of work on the surroundings. 49.1 kJ 9.00times 10^2kJ -49.1kJ -50.9kJ -9.00times 10^2kJ

Here's how to calculate the change in internal energy:<br /><br />**Understanding the First Law of Thermodynamics**<br /><br />The First Law of Thermodynamics states that 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):<br /><br />ΔU = q - w<br /><br />**Sign Conventions**<br /><br />* **q (heat):** Positive if heat is *added* to the system, negative if heat is *released* by the system.<br />* **w (work):** Positive if work is done *on* the system, negative if work is done *by* the system.<br /><br />**Applying the Formula**<br /><br />1. **Convert units:** Since the heat is given in kJ and the work in J, we need to convert them to the same unit. Let's convert the work to kJ:<br /><br /> 855 J * (1 kJ / 1000 J) = 0.855 kJ<br /><br />2. **Substitute values:** The system is giving off heat, so q is negative. The system is doing work on the surroundings, so w is negative.<br /><br /> ΔU = -50.0 kJ - (-0.855 kJ)<br /><br />3. **Calculate:**<br /><br /> ΔU = -50.0 kJ + 0.855 kJ = -49.145 kJ<br /><br />4. **Round to the correct number of significant figures:** The least number of decimal places in the given values is one (50.0 kJ), so we round our answer to one decimal place:<br /><br /> ΔU = -49.1 kJ<br /><br />**Therefore, the correct answer is -49.1 kJ.**<br />