We can use Charles's law to solve this problem. Charles's law states that the volume of a gas is directly proportional to its temperature, when the pressure is held constant. Mathematically, it can be expressed as:

V₁/T₁ = V₂/T₂

where V₁ and T₁ represent the initial volume and temperature, respectively, and V₂ and T₂ represent the final volume and temperature, respectively.

In this case, we know that the initial volume (V₁) is 20 m³, the initial temperature (T₁) is 27 °C, and the final temperature (T₂) is 177 °C. We need to find the final volume (V₂).

First, we need to convert the temperatures to Kelvin. We add 273 to each temperature:

T₁ = 27 °C + 273 = 300 K

T₂ = 177 °C + 273 = 450 K

Now we can substitute the values into Charles's law equation:

V₁/T₁ = V₂/T₂

20 m³ / 300 K = V₂ / 450 K

Solving for V₂, we get:

V₂ = (20 m³ * 450 K) / 300 K

V₂ = 30 m³

Therefore, the new volume occupied by the gas is 30 m³.