Answer:
To determine the new pressure of the gas, we can use Charles's Law, which states that the volume of a given amount of gas held at constant pressure is directly proportional to its temperature.
Charles's Law equation:
(V₁ / T₁) = (V₂ / T₂)
Where:
V₁ = Initial volume
T₁ = Initial temperature
V₂ = Final volume (held constant)
T₂ = Final temperature
In this case, the initial volume and the final volume are held constant, so we can rewrite the equation as:
(T₁ / P₁) = (T₂ / P₂)
Where:
P₁ = Initial pressure
P₂ = Final pressure
Now let's substitute the given values:
T₁ = 25°C = 25 + 273.15 = 298.15 K
P₁ = 125 kPa
T₂ = 127°C = 127 + 273.15 = 400.15 K
Plugging these values into the equation:
(298.15 K / 125 kPa) = (400.15 K / P₂)
To solve for P₂, we can cross-multiply and then divide:
(298.15 K) * P₂ = (125 kPa) * (400.15 K)
P₂ = (125 kPa * 400.15 K) / 298.15 K
P₂ ≈ 167.03 kPa
Therefore, the new pressure of the gas is approximately 167.03 kPa when the temperature is increased to 127°C while keeping the volume constant.