Question

What is the change in internal energy of a system if \(500\,\text{J}\) of heat is added and \(200\,\text{J}\) of work is done by the system?

• A. \(300\,\text{J}\)
• B. \(700\,\text{J}\)
• C. \(200\,\text{J}\)
• D. \(500\,\text{J}\)

Hint:

In thermodynamics sign convention: Heat added to the system is positive, and work done by the system is subtracted.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This problem relates heat, work, and internal energy in a thermodynamic process.
The topic is Thermodynamics.
Step 2: Key Formula or Approach:
Apply the First Law of Thermodynamics:
\[ \Delta U = Q - W \]
Note: \( Q \) is positive if heat is added, and \( W \) is positive if work is done by the system.
Step 3: Detailed Explanation:
Given values with sign conventions:
Heat added to the system, \( Q = +500\,\text{J} \).
Work done by the system, \( W = +200\,\text{J} \).
Using the formula:
\[ \Delta U = 500 - 200 \]
Step 4: Final Answer:
\[ \Delta U = 300\,\text{J} \]