Question
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
Solution
4.5
(274 Votes)
Quentin
Elite · Tutor for 8 years
Answer
Here's how to calculate the change in internal energy:**Understanding the First Law of Thermodynamics**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):ΔU = q - w**Sign Conventions*** **q (heat):** Positive if heat is *added* to the system, negative if heat is *released* by the system.* **w (work):** Positive if work is done *on* the system, negative if work is done *by* the system.**Applying the Formula**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: 855 J * (1 kJ / 1000 J) = 0.855 kJ2. **Substitute values:** The system is giving off heat, so q is negative. The system is doing work on the surroundings, so w is negative. ΔU = -50.0 kJ - (-0.855 kJ)3. **Calculate:** ΔU = -50.0 kJ + 0.855 kJ = -49.145 kJ4. **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: ΔU = -49.1 kJ**Therefore, the correct answer is -49.1 kJ.**