Question

The mathematical statement of the first law of thermodynamics with the usual notation is

• A. \(\Delta U = w - q\)
• B. \(q = \Delta U \times w\)
• C. \(W = q + \Delta U\)
• D. \(\Delta U = q / w\)
• E. \(\Delta U = q + w\)

Hint:

In older physics textbooks, you might see \(\Delta U = q - w\).
This is because in physics, work is often defined as work done by the system.
In modern chemistry (IUPAC), we always use \(\Delta U = q + w\).

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
The First Law of Thermodynamics is essentially the law of conservation of energy applied to thermodynamic systems.
It states that energy can neither be created nor destroyed, only transformed from one form to another.

Step 3: Detailed Explanation:
For a closed system, the change in internal energy (\(\Delta U\)) is equal to the heat (\(q\)) added to the system plus the work (\(w\)) done on the system.
According to IUPAC convention:
- Heat absorbed by the system = \(+q\)
- Work done on the system = \(+w\)
The mathematical expression is:
\[ \Delta U = q + w \]
This means the total energy of an isolated system remains constant.

Step 4: Final Answer:
The mathematical statement is \(\Delta U = q + w\).