A balloon has a volume of 175 cm3 at 19ºC. At what temperature will the volume of the balloon have increased by 25.0% (at constant pressure).
(V1/T1) (V2/T2)
T must be in kelvin.
V1 = 175 cc; V2 = 175 + (175 x 0.25)
To find the temperature at which the volume of the balloon has increased by 25%, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin at constant pressure.
Step 1: Convert the initial volume to Kelvin.
The equation we can use is:
V₁ / T₁ = V₂ / T₂
Where V₁ is the initial volume, T₁ is the initial temperature, V₂ is the final volume (increase of 25%), and T₂ is the final temperature.
Given:
Initial volume (V₁) = 175 cm³
Initial temperature (T₁) = 19°C
To convert the temperature to Kelvin, we need to add 273.15 to the Celsius value:
T₁ = 19°C + 273.15 = 292.15 K
Step 2: Calculate the final volume.
We want to find the final temperature (T₂) that results in a 25% increase in volume.
Let's calculate the final volume:
Final volume (V₂) = Initial volume (V₁) + (25% of initial volume)
= 175 cm³ + (0.25 * 175 cm³)
= 175 cm³ + 43.75 cm³
= 218.75 cm³
Step 3: Rearrange the Charles's Law equation to solve for the final temperature (T₂).
V₁ / T₁ = V₂ / T₂
T₂ = T₁ * (V₂ / V₁)
Now we can substitute the values we have:
T₂ = 292.15 K * (218.75 cm³ / 175 cm³)
Step 4: Calculate the final temperature (T₂).
T₂ ≈ 365.19 K
Therefore, the temperature at which the volume of the balloon will increase by 25% (at constant pressure) is approximately 365.19 K.
To find the temperature at which the volume of the balloon will have increased by 25.0%, we can use Charles's law, which states that the volume of a gas is directly proportional to its temperature (at constant pressure).
First, let's calculate the initial volume of the balloon using the given information. The initial volume is given as 175 cm³ at a temperature of 19ºC.
Now, we need to calculate the volume increase. Since the increase is given as a percentage, we can find the volume increase by multiplying the initial volume (175 cm³) by 25.0% (or 0.25).
Volume increase = 175 cm³ * 0.25 = 43.75 cm³
Next, we need to find the final volume of the balloon after the increase. The final volume is calculated by adding the volume increase to the initial volume.
Final volume = Initial volume + Volume increase = 175 cm³ + 43.75 cm³ = 218.75 cm³
Now that we have the final volume, we can use Charles's law to find the temperature at which this volume will be reached. Charles's law states that the volume is directly proportional to the temperature (at constant pressure).
The formula for Charles's law is: V₁ / T₁ = V₂ / T₂
Where:
V₁ = Initial volume
T₁ = Initial temperature
V₂ = Final volume
T₂ = Final temperature
Rearranging the formula, we have:
T₂ = (T₁ * V₂) / V₁
Plugging in the values:
T₂ = (19ºC * 218.75 cm³) / 175 cm³
Simplifying the equation:
T₂ = (19 * 218.75) / 175
T₂ = 23.68ºC
Therefore, the temperature at which the volume of the balloon will have increased by 25.0% (at constant pressure) is approximately 23.68ºC.