Question

Write the mathematical equation of first law of thermodynamics for following processes : (a) Isochoric process, (b) Adiabatic process

Hint:

Isochoric $\rightarrow$ constant volume $\rightarrow$ no work.
Adiabatic $\rightarrow$ insulated system $\rightarrow$ no heat.

Answer 1

Step 1: Understanding the Concept:
The First Law of Thermodynamics is \(\Delta U = q + w\). For a pressure-volume work, \(w = -P \Delta V\).
Step 3: Detailed Explanation:
In an isochoric process, the volume of the system remains constant (\(V = \text{constant}\)), which means \(\Delta V = 0\).
Substituting this into the work equation: \(w = -P \times 0 = 0\).
Applying this to the First Law:
\[ \Delta U = q + 0 \]
\[ \Delta U = q_v \]
This indicates that the entire heat supplied to the system is used to increase its internal energy.
Step 4: Final Answer: The equation for an isochoric process is \(\Delta U = q_v\).