Question

A helium-filled balloon has a volume of 1.6 m3 . As it rises in the Earth’s atmosphere, its volume changes. What is its new volume if its original temperature and pressure are 16◦C and 1.3 atm and its final temperature and pressure are −41◦C and 1.2 atm? Answer in units of m

Answer 1

Answer: 1.39 m3

Explanation:

If we consider the helium to be an ideal gas, at any condition, we can apply the Ideal Gas Equation as follows:

P V = n R T

Taking the initial state as (1), we can write:

P1V1 = n R T1 (1)

In the initial state, we have P= 1.3 atm, V=1.6 m3, and T= 273 K + 16 K =289 K.

Let’s call (2) to the final state, so we can write as follows:

P2V2 = n R T2 (2)

In the final state, our givens are P= 1.2 atm, and T= 273 K -41 K = 232 K

So, dividing both sides in (1) and (2), we can solve for V2, as follows:

V2 = (1.3 atm. 1.6 m3.232 K) / 1.2 atm. 289 K = 1.39 m3