To solve this problem, we can use the ideal gas law, which states that the product of the pressure (P), volume (V), and temperature (T) of a gas is constant when the amount of gas and the conditions are held constant. The equation can be written as:
P₁V₁/T₁ = P₂V₂/T₂
where: P₁ and P₂ are the initial and final pressures, respectively (held constant in this case), V₁ and V₂ are the initial and final volumes, respectively, T₁ is the initial temperature, and T₂ is the final temperature that we need to find.
Given: V₁ = 40 cm³ V₂ = 54.70 cm³ T₁ = 0°C = 273.15 K (conversion from Celsius to Kelvin)
Let's assume the pressure remains constant, so P₁ = P₂.
Plugging in the values into the ideal gas law equation:
P₁V₁/T₁ = P₂V₂/T₂
Since P₁ = P₂, we can cancel out the pressure terms:
V₁/T₁ = V₂/T₂
Rearranging the equation to solve for T₂:
T₂ = (V₂ × T₁) / V₁
Substituting the given values:
T₂ = (54.70 cm³ × 273.15 K) / 40 cm³
Calculating the result:
T₂ ≈ 372.1 K
Therefore, the temperature at which the volume expands to 54.70 cm³ under the same conditions of pressure is approximately 372.1 Kelvin.