a ballon is filled with hydrogen at given pressure at 20 degree celsius .what fraction of gas will escape out of the ballon if temperature rises to 40 degree celsius at constant pressue.
To determine the fraction of gas that will escape from the balloon when the temperature rises from 20 degrees Celsius to 40 degrees Celsius at constant pressure, we can use Charles' Law. This law states that the volume of a gas is directly proportional to its temperature, assuming the pressure and the amount of gas remain constant.
The equation for Charles' Law is as follows:
V1 / T1 = V2 / T2
Where:
- V1 is the initial volume of the gas
- T1 is the initial temperature of the gas
- V2 is the final volume of the gas
- T2 is the final temperature of the gas
Since we are given that the pressure remains constant, we can rearrange the equation to solve for the ratio of volumes:
V2 / V1 = T2 / T1
Now, let's plug in the given values:
T1 = 20 degrees Celsius
T2 = 40 degrees Celsius
Now, we need to assume an initial and final volume. Let's say the initial volume is V1 and the final volume is V2.
Using the equation, we can solve for the ratio of volumes:
V2 / V1 = (40 + 273) / (20 + 273)
The temperatures need to be converted to Kelvin by adding 273 to them.
Simplifying:
V2 / V1 = 313 / 293
Finally, we have the ratio of volumes. The fraction of gas that will escape can be calculated by subtracting this ratio from 1:
Fraction of gas that will escape = 1 - (V2 / V1)
Please note that this calculation assumes ideal gas behavior and does not account for other factors that may affect the escape of gas, such as the balloon's elasticity or the presence of any leaks.