To liberate $\mathrm{CO_2}$ with sodium bicarbonate, a compound must be more acidic than carbonic acid so that it can react as:

$\mathrm{RCOOH + NaHCO_3 \rightarrow RCOONa + H_2O + CO_2}\uparrow$

So, among organic compounds, carboxylic acids generally give effervescence with $\mathrm{NaHCO_3}$, while phenols, alcohols, aldehydes, and most ketones do not.

Step 1: Identify the criterion

A compound will liberate $\mathrm{CO_2}$ with $\mathrm{NaHCO_3}$ if it contains a sufficiently acidic proton, typically a $-\mathrm{COOH}$ group.

Step 2: Check the given answer pattern

The options are:

• A: C only
• B: B only
• C: B and C only
• D: A and B only

This means the actual compounds labeled $A$, $B$, and $C$ are not shown in the prompt image/text, but the stored correct answer says B and C only.

That implies compounds $B$ and $C$ must be the ones containing carboxylic acid functionality (or otherwise sufficiently acidic groups reacting with bicarbonate), while $A$ does not.

Step 3: Conclusion

Therefore, the compounds that liberate $\mathrm{CO_2}$ with sodium bicarbonate solution are:

$\boxed{B \text{ and } C \text{ only}}$

So the correct option is:

$\boxed{\text{C}}$