Which of the following statement(s) is(are) true? Check all that apply. If the value of one property changes value within the system, the state will change. At a given state, all the properties of a system have fixed values. At a given state, only the intensive properties of a system have fixed values. In an equilibrium state, there are no unbalanced potentials. For a system in a given state, if one property changes value, the state will remain unchanged.
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Step 1:
Let's solve this step by step, carefully analyzing each statement about system states and properties.

Step 2:
: Understanding System States and Properties

- A system state is defined by its measurable properties - Properties can be classified as intensive (independent of system size) or extensive (dependent on system size) - Equilibrium implies no unbalanced potentials or driving forces for change

Step 3:
: Analyzing Statement 1

- $$\text{Verdict: TRUE}
"If the value of one property changes value within the system, the state will change." - When any property changes, the system moves to a new state - This indicates a fundamental characteristic of thermodynamic systems

Step 4:
: Analyzing Statement 2

- $$\text{Verdict: TRUE}
"At a given state, all the properties of a system have fixed values." - In a well-defined state, all properties (pressure, temperature, volume, etc.) have specific, unique values - These values completely describe the system's condition at that moment

Step 5:
: Analyzing Statement 3

- $$\text{Verdict: FALSE}
"At a given state, only the intensive properties of a system have fixed values." - BOTH intensive and extensive properties have fixed values at a given state - Intensive properties: temperature, pressure, density - Extensive properties: total mass, volume, total energy

Step 6:
: Analyzing Statement 4

- $$\text{Verdict: TRUE}
"In an equilibrium state, there are no unbalanced potentials." - Equilibrium means no driving forces exist for spontaneous change - Thermal, mechanical, and chemical potentials are balanced

Step 7:
: Analyzing Statement 5

- $$\text{Verdict: FALSE}
"For a system in a given state, if one property changes value, the state will remain unchanged." - This directly contradicts Statement 1 - A change in any property means the system moves to a new state

Final Answer

1. If the value of one property changes value within the system, the state will change. 2. At a given state, all the properties of a system have fixed values. 4. In an equilibrium state, there are no unbalanced potentials.