a balloon has a volume of 2.0 L at room temperature (27 degrees celsius). at what temperature would the balloon have a volume of 2.0L?
same volume both times
To determine the temperature at which the balloon would have a volume of 2.0 L, we need to use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure and amount of gas remain constant.
Charles's Law can be expressed as:
V₁ / T₁ = V₂ / T₂
Where:
V₁ and T₁ are the initial volume and temperature of the gas (in this case, the balloon).
V₂ and T₂ are the final volume and temperature of the gas we want to find.
In our case, we are given that the initial volume (V₁) is 2.0 L at a temperature (T₁) of 27 degrees Celsius. We want to find the temperature (T₂) at which the volume (V₂) is also 2.0 L.
Let's substitute the known values into the formula to solve for T₂:
V₁ / T₁ = V₂ / T₂
Plugging in the known values:
2.0 L / 27 °C = 2.0 L / T₂
To isolate T₂, we can cross-multiply:
2.0 L * T₂ = 2.0 L * 27 °C
Now, divide both sides by 2.0 L:
T₂ = (2.0 L * 27 °C) / 2.0 L
The liters cancel out, leaving us with:
T₂ = 27 °C
Hence, the temperature at which the balloon would have a volume of 2.0 L is 27 degrees Celsius, which is the same as the original temperature given in the question.