Answer :
In an ideal cyclic process within thermodynamics, several principles come into play, particularly the first law of thermodynamics. To analyze the situation, let's break down the concepts and determine the correct statement.
First, let's recall the first law of thermodynamics for a closed system, which states:
[tex]\[ \Delta U = Q - W \][/tex]
where:
- [tex]\(\Delta U\)[/tex] is the change in internal energy of the system,
- [tex]\(Q\)[/tex] is the energy added to the system as heat,
- [tex]\(W\)[/tex] is the work done by the system.
In an ideal cyclic process, the system undergoes a series of transformations but returns to its initial state at the end of the cycle. This cyclical return to the starting point implies that the change in internal energy over one complete cycle is zero. Therefore, for a cyclic process:
[tex]\[ \Delta U = 0 \][/tex]
Given that [tex]\(\Delta U = 0\)[/tex], we can substitute it into the first law of thermodynamics, resulting in:
[tex]\[ 0 = Q - W \][/tex]
This can be rearranged to show that the net work done ([tex]\(W\)[/tex]) over a cycle is equal to the net energy transferred as heat ([tex]\(Q\)[/tex]):
[tex]\[ W = Q \][/tex]
Upon analyzing the given options:
- Option A states that the energy added as heat is converted entirely to work. This suggests a one-to-one conversion in a single process, not necessarily over a complete cycle.
- Option B states that the net work is greater than the net transfer of energy as heat. This contradicts our derived equation.
- Option C states that the net work done equals the net transfer of energy as heat. This matches our derived equation perfectly.
- Option D states that the net work is less than the net transfer of energy as heat. This also contradicts our derived equation.
Based on the analysis and the principles of thermodynamics, the correct statement regarding an ideal cyclic process is:
Option C: The net work done equals the net transfer of energy as heat.
First, let's recall the first law of thermodynamics for a closed system, which states:
[tex]\[ \Delta U = Q - W \][/tex]
where:
- [tex]\(\Delta U\)[/tex] is the change in internal energy of the system,
- [tex]\(Q\)[/tex] is the energy added to the system as heat,
- [tex]\(W\)[/tex] is the work done by the system.
In an ideal cyclic process, the system undergoes a series of transformations but returns to its initial state at the end of the cycle. This cyclical return to the starting point implies that the change in internal energy over one complete cycle is zero. Therefore, for a cyclic process:
[tex]\[ \Delta U = 0 \][/tex]
Given that [tex]\(\Delta U = 0\)[/tex], we can substitute it into the first law of thermodynamics, resulting in:
[tex]\[ 0 = Q - W \][/tex]
This can be rearranged to show that the net work done ([tex]\(W\)[/tex]) over a cycle is equal to the net energy transferred as heat ([tex]\(Q\)[/tex]):
[tex]\[ W = Q \][/tex]
Upon analyzing the given options:
- Option A states that the energy added as heat is converted entirely to work. This suggests a one-to-one conversion in a single process, not necessarily over a complete cycle.
- Option B states that the net work is greater than the net transfer of energy as heat. This contradicts our derived equation.
- Option C states that the net work done equals the net transfer of energy as heat. This matches our derived equation perfectly.
- Option D states that the net work is less than the net transfer of energy as heat. This also contradicts our derived equation.
Based on the analysis and the principles of thermodynamics, the correct statement regarding an ideal cyclic process is:
Option C: The net work done equals the net transfer of energy as heat.
