application of pressure law (Charles law)

Question 1

📝 Problem:
A balloon initially has a volume of 10.0 liters at a temperature of 20.0°C. If the temperature of the balloon is increased to 50.0°C while keeping the pressure constant, what will be the new volume of the balloon?

Answer 1

🧠 Solution:
According to Charles’s Law, when the pressure of a gas is held constant, the volume of the gas is directly proportional to its absolute temperature.

Given:
- Initial volume (( V_1 )) = 10.0 liters
- Initial temperature (( T_1 )) = 20.0°C
- Final temperature (( T_2 )) = 50.0°C (temperature increased)

First, we need to convert the temperatures to Kelvin since Charles’s Law requires temperatures in Kelvin scale:
[ T(K) = T(°C) + 273.15 ]

For initial temperature (( T_1 )):
[ T_1(K) = 20.0°C + 273.15 = 293.15 \, \text{K} ]

For final temperature (( T_2 )):
[ T_2(K) = 50.0°C + 273.15 = 323.15 \, \text{K} ]

Now, we can use Charles’s Law equation:
[ \frac{V_1}{T_1} = \frac{V_2}{T_2} ]

Substitute the given values:
[ \frac{10.0 \, \text{L}}{293.15 \, \text{K}} = \frac{V_2}{323.15 \, \text{K}} ]

Cross multiply:
[ 10.0 \times 323.15 = V_2 \times 293.15 ]

[ V_2 = \frac{10.0 \times 323.15}{293.15} ]

[ V_2 \approx 10.99 \, \text{L} ]

So, the new volume of the balloon (( V_2 )) is approximately 10.99 liters.

✨ Answer:
The new volume of the balloon is approximately 10.99 liters.