To find the new temperature of the sodium gas, we start with the initial temperature and then subtract the additional cooling.
The initial temperature is \( -78.5°C \).
Next, we cool it down by \( 194.65°C \):
\[ \text{New Temperature} = -78.5°C - 194.65°C \]
Calculating this:
\[ -78.5 - 194.65 = -273.15°C \]
So, the new temperature of the sodium gas is:
\[ \boxed{-273.15°C} \]