What is the pressure inside such a balloon (in atm) if it starts out at sea level with a temperature of 12.8°C and rises to an altitude where its volume is twenty-two times the original volume and its temperature is −47.7°C? (Enter your answer to at least 3 decimal places)

The final pressure inside the balloon will be .

Explanation:

Given initial temperature of the balloon is

And the final temperature of the balloon is

Initially, the balloon is at atmospheric pressure and volume be

And the final pressure in the balloon is and the volume be

Also, it is given in the question that the final volume became twenty-two times the original volume.

We can write

Now, using ideal gas equation.

Where, is the gas constant. And is moles of substance inside the balloon.

In our problem the value of will be the same for both cases. Also, is the gas constant.

Also, we have from the question.

We need to convert the temperature from to Kelvin.

Plug these values we get,

So, the final pressure inside the balloon will be .