For a closed system undergoing a thermodynamic cycle, the first law states which of the following?

Explanation:

In thermodynamics, the first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. It is one of the fundamental principles of thermodynamics and states that energy cannot be created or destroyed in an isolated system. The first law is often expressed mathematically as:

ΔU = Q - W

where:

• ΔU is the change in internal energy of the system.
• Q is the heat added to the system.
• W is the work done by the system.

For a closed system undergoing a thermodynamic cycle, the first law of thermodynamics states that the net work done by the system over one complete cycle is equal to the net heat added to the system over the cycle. This is because, over a complete cycle, the system returns to its initial state, meaning the change in internal energy (ΔU) is zero.

Therefore, the correct interpretation of the first law in the context of a thermodynamic cycle is:

Net work done equals net heat transfer.

This is option 1 from the given choices.

Correct Option Analysis:

For a closed system undergoing a thermodynamic cycle, the first law of thermodynamics can be written as:

ΔU = Q - W

During a complete cycle, the system returns to its initial state, which means the change in internal energy (ΔU) is zero:

ΔU = 0

Substituting this into the first law equation gives:

0 = Q - W

Rearranging this equation, we find:

Q = W

This signifies that the net heat added to the system (Q) over the cycle is equal to the net work done by the system (W) over the cycle.

In other words, the energy added to the system as heat is completely converted into work during the cycle, which aligns with the principle of conservation of energy.

Important Information for Analysis of Other Options:

Option 2: Entropy always increases.

This statement is not correct in the context of the first law of thermodynamics. The concept of entropy is related to the second law of thermodynamics, which states that the entropy of an isolated system always increases over time, and processes occur in the direction of increasing entropy. However, this does not directly pertain to the first law, which is concerned with energy conservation.

Option 3: Pressure and temperature are inversely related.

This statement is not a general principle of thermodynamics. The relationship between pressure and temperature depends on the specific thermodynamic process being considered. For example, in an isothermal process, the temperature remains constant, while pressure can change. In an adiabatic process, both pressure and temperature can change. Therefore, pressure and temperature are not universally inversely related.

Option 4: Internal energy remains constant.

While the change in internal energy (ΔU) over a complete cycle is zero for a closed system, it does not mean that internal energy remains constant throughout the cycle. During different stages of the cycle, the internal energy can change due to heat transfer and work interactions. The first law of thermodynamics indicates the net change in internal energy over a cycle is zero, but internal energy can vary within individual processes of the cycle.

In summary, the correct interpretation of the first law of thermodynamics for a closed system undergoing a thermodynamic cycle is that the net work done by the system equals the net heat transfer into the system (option 1). The other options are either related to different thermodynamic principles or are not universally applicable.