91Ó°ÊÓ

In the realm of thermodynamics, the concept of work is pivotal. Work is a form of energy transfer between a system and its surroundings. When we talk about work done on a system, it refers to energy being transferred into the system. This can cause changes in pressure, volume, or even the internal energy of the system.

It's crucial to understand how the sign of work is interpreted. When work is done on the system, we consider it to be negative. This might seem counterintuitive since we're adding energy, but in thermodynamics, we focus on energy leaving the system. Thus, if the system gains energy through work, we write it as a negative, signifying that energy isn't being released by the system.

In the exercise given, 200 J of work is performed on the system. This means the system receives energy from an external source. In terms of first law equations, this is expressed as \( W = -200 \, \text{J} \). Understanding this notation will help in solving numerous thermodynamic problems.

Heat, another form of energy transfer, plays a crucial role in thermodynamics. When heat is extracted from a system, it means energy is being removed. This energy removal can lead to a temperature drop, effect on phase changes, or other transformations within the system.

Similar to work, the direction of heat transfer determines its sign. When heat is removed, it is considered negative because the system's energy is decreasing. In our exercise, 70.0 cal of heat is extracted. First, we convert calories to joules using the conversion factor \( 1 \text{ cal} = 4.184 \text{ J} \). Therefore, \( 70.0 \text{ cal} = 292.88 \text{ J} \).

With this conversion, the heat extracted from the system is \( Q = -292.88 \, \text{J} \). Recognizing this negative sign is important, making it clear that the system is losing energy in terms of thermal motion.

The concept of internal energy change, represented by \( \Delta E_{\text{int}} \), is at the heart of the first law of thermodynamics. This principle links the work done and heat exchanged by a system to its change in internal energy.

According to the first law, the change in a system's internal energy is the difference between the heat added to the system \( Q \) and the work done by the system \( W \). Mathematically, this is expressed as:

• \( \Delta E_{\text{int}} = Q - W \)

In our exercise, we already have \( Q = -292.88 \, \text{J} \) and \( W = -200 \, \text{J} \). Plugging in these values:

• \( \Delta E_{\text{int}} = -292.88 \, \text{J} - (-200 \, \text{J}) = -92.88 \, \text{J} \)

This negative value indicates a decrease in the system's internal energy. It reflects the overall effect of heat being removed and work done on the system. As you tackle thermodynamics problems, always consider these energy transfers and how they affect the internal state of the system.