when a heat is rejected by a system what will be q according to sign convention?

When a system rejects heat, the sign convention typically used in thermodynamics indicates that the heat transfer, denoted as \( q \), is negative. This is based on the first law of thermodynamics, which states that energy can neither be created nor destroyed, only transformed from one form to another. Let’s break this down further.

Understanding Heat Transfer

In thermodynamics, heat transfer can occur in two main ways: heat can be absorbed by a system or rejected by it. The sign convention helps us keep track of energy flow. Here’s how it works:

• Heat Absorption: When a system absorbs heat from its surroundings, \( q \) is considered positive. This means the internal energy of the system increases.
• Heat Rejection: Conversely, when a system rejects heat, \( q \) is negative. This indicates that the internal energy of the system decreases.

Applying the Sign Convention

Let’s consider a practical example to illustrate this concept. Imagine a steam engine that is performing work. As the engine operates, it converts thermal energy into mechanical energy. During this process, the engine releases some heat to its surroundings. According to our sign convention:

• When the engine releases heat, we assign a negative value to \( q \) (e.g., \( q = -500 \, \text{J} \)).
• This negative value indicates that the system is losing energy in the form of heat.
• As a result, the internal energy of the steam engine decreases, which can affect its performance if too much heat is rejected.

Why This Matters

Understanding the sign convention for heat transfer is crucial in thermodynamics because it allows engineers and scientists to analyze energy systems accurately. It helps in calculating changes in internal energy, work done by or on the system, and overall efficiency. For instance, in a refrigeration cycle, the refrigerant absorbs heat from the environment (positive \( q \)) and then rejects heat to the outside (negative \( q \)), which is essential for the cooling process.

In summary, when a system rejects heat, the value of \( q \) is negative according to the standard sign convention in thermodynamics. This convention is vital for analyzing energy exchanges and ensuring accurate calculations in various applications, from engines to refrigerators.