Which of the following is correct regarding the internal energy of a substance ?

Options

A. It is the sum of all microscopic energies
B. It is dependent on temperature
C. Its change can be estimated by experiment
D. All of these are correct

Answer

To determine which statements regarding the internal energy of a substance are correct, we will analyze each statement step by step.

### Step 1: Understanding Internal Energy
**Definition**: Internal energy (U) is defined as the total energy contained within a substance, which includes all forms of microscopic energy such as kinetic and potential energy of the particles.

**Conclusion**: The first statement, which claims that internal energy is the sum of all microscopic energies, is correct.

### Step 2: Dependence on Temperature
**Explanation**: The internal energy of a substance is indeed dependent on temperature. As temperature increases, the kinetic energy of the particles also increases. Mathematically, the average kinetic energy of particles in a gas can be expressed as:
\[ \text{Average Kinetic Energy} = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.

**Conclusion**: The second statement, which states that internal energy is dependent on temperature, is also correct.

### Step 3: Experimental Estimation
**Explanation**: Internal energy can be estimated experimentally. One common method is using a bomb calorimeter, which measures the heat change in a reaction to determine the internal energy change (ΔU). The relationship can be expressed as:
\[ \Delta U = n C_v \Delta T \]
where \( n \) is the number of moles, \( C_v \) is the molar heat capacity at constant volume, and \( \Delta T \) is the change in temperature.

**Conclusion**: The third statement, which claims that internal energy can be estimated by experiment, is also correct.

### Final Conclusion
Since all three statements regarding the internal energy of a substance are correct, the final answer is that all of the statements are correct.

### Summary of Correct Statements:
1. Internal energy is the sum of all microscopic energies.
2. Internal energy is dependent on temperature.
3. Internal energy can be estimated by experiment.