### Step-by-Step Solution
**Step 1: State the First Law of Thermodynamics**
The First Law of Thermodynamics states that the change in the internal energy of a system (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W). Mathematically, it can be expressed as:
\[
\Delta U = Q - W
\]
This law essentially expresses the principle of conservation of energy, indicating that energy can neither be created nor destroyed, only transformed from one form to another.
**Step 2: Explain the Components of the First Law**
In the equation ΔU = Q - W:
- **ΔU** is the change in internal energy of the system.
- **Q** is the heat added to the system. If heat is removed, Q is negative.
- **W** is the work done by the system on its surroundings. If work is done on the system, W is negative.
**Step 3: Discuss the Isothermal Process**
An isothermal process is one in which the temperature of the system remains constant (ΔT = 0). For an ideal gas, the internal energy (U) is a function of temperature only. Therefore, if the temperature does not change, the change in internal energy is:
\[
\Delta U = 0
\]
Using the First Law:
\[
0 = Q - W
\]
This implies:
\[
Q = W
\]
In an isothermal expansion, the gas does work on the surroundings, and thus heat is absorbed from the surroundings to maintain constant temperature. Conversely, during isothermal compression, work is done on the gas, and it releases heat to the surroundings.
**Step 4: Discuss the Adiabatic Process**
An adiabatic process is one in which no heat is exchanged with the surroundings (Q = 0). Thus, applying the First Law:
\[
\Delta U = Q - W
\]
becomes:
\[
\Delta U = 0 - W
\]
or:
\[
\Delta U = -W
\]
This means that any work done by the system results in a decrease in internal energy, leading to a drop in temperature. Conversely, if work is done on the system, the internal energy increases, leading to a rise in temperature.
### Summary of Applications
- **Isothermal Process:**
- ΔU = 0, hence Q = W.
- Heat absorbed equals work done by the system.
- **Adiabatic Process:**
- Q = 0, hence ΔU = -W.
- Work done by the system results in a decrease in internal energy and temperature.
