Concept:
Water gas is a mixture of carbon monoxide (CO) and hydrogen (H$_2$). It is an important industrial fuel and also used as a reducing agent. It is produced by passing steam over red hot carbon (coke). The key reaction involved is:
\[
\text{C (s)} + \text{H}_2\text{O (g)} \rightarrow \text{CO (g)} + \text{H}_2\text{(g)}
\]
This is an endothermic reaction, meaning heat must be supplied continuously to maintain the process.
Step 1: Understanding the formation of water gas
When steam is passed over red hot coke (carbon), the above reaction takes place producing a mixture of CO and H$_2$, which is called water gas.
Step 2: Analyze each option
Option (A): Passing steam over red hot coke
This directly corresponds to the reaction:
\[
\text{C} + \text{H}_2\text{O} \rightarrow \text{CO} + \text{H}_2
\]
Hence, this produces water gas. Correct
Option (B): Passing steam and air over red hot coke
This produces producer gas, not water gas. Air introduces nitrogen and oxygen:
\[
\text{C} + \text{O}_2 \rightarrow \text{CO}_2, \quad \text{CO}_2 + \text{C} \rightarrow 2\text{CO}
\]
Resulting gas contains CO, N$_2$, and small H$_2$. Incorrect
Option (C): Burning coke in excess air
Produces mainly CO$_2$, not water gas:
\[
\text{C} + \text{O}_2 \rightarrow \text{CO}_2
\]
Incorrect
Option (D): Burning coke in limited air
Produces CO (producer gas component), but no hydrogen:
\[
2\text{C} + \text{O}_2 \rightarrow 2\text{CO}
\]
Incorrect
Option (E): Both (A) and (B)
Since (B) is incorrect, this option is also incorrect.
Final Conclusion:
Only passing steam over red hot coke produces water gas. Hence, the correct answer is:
\[
\boxed{(A)}
\]