# Entropy and a baloon of gas

• Gemstone
In summary, Me and my friend were stuck on an assignment that required us to calculate the total entropy of a balloon filled with 10 mol of helium, going from a temperature of 25 degrees Celsius to -5 degrees Celsius. We were able to solve it with the help of the first law of thermodynamics and the ideal gas equation.
Gemstone
Me and a friend has recently fallen into a dead-end with an assignment we have, because we can't calculate the total entropy of a baloon filled with Helium.

Basicly, the assignment goes:
We have a baloon with 10 mol of Helium, inside a house with a temperature of 25 degrees celcius (that is, 298 kelvin). Now, we take the baloon outside to a temperature of -5 degrees clecius (268 kelvin).

Now, we're supposed to calculate the total entropy of the baloon and the environment. Anyone willing to help us out?

We've this far deducted that the pressure is 101,3 KPa (1 atmosphere)... which is by far the longest we've come.

Any help is appreiciated

Entropy is:

S=kLn(Ω)

Where Ω is the multiplicity of the system.

Also. ∆S=∫dQ/t

This should help get you started.

I think starting from the statistical definition of entropy would be a bit much for this problem. =P I think the formulae for ideal gases are well known enough that they can just be used right from the start.

So, since you're dealing with helium, you can indeed treat the gas in the balloon as an ideal gas.

For an ideal gas, you know how pressure and volume relate: PV = nRT, and there's also a formula for the energy of an ideal monatomic gas, E = 3nRT/2. From this you can derive an equation for the entropy change given the volume change and the temperature change (recall that in these formulae temperature must be measured in Kelvins).

Hopefully that helps.

Thank you for your help :) We managed to solve the equation in the end

## 1. What is entropy?

Entropy is a measure of the disorder or randomness in a system. In simple terms, it is the measure of how much energy is spread out or dispersed within a system.

## 2. How does entropy relate to a balloon of gas?

In the context of a balloon of gas, entropy can be thought of as the measure of how the gas molecules are distributed within the balloon. As the gas molecules move around and collide with each other, they become more disordered and the entropy of the system increases.

## 3. Why does a balloon of gas expand?

A balloon of gas expands because of the increase in entropy. As the gas molecules move around and collide with each other, they take up more space and the volume of the balloon increases.

## 4. How does temperature affect the entropy of a balloon of gas?

Temperature directly affects the entropy of a balloon of gas. As the temperature increases, the gas molecules have more energy and move around more, increasing the disorder and therefore the entropy of the system.

## 5. Can the entropy of a balloon of gas ever decrease?

According to the second law of thermodynamics, the entropy of a closed system (such as a balloon of gas) will always increase or remain constant. It is highly unlikely for the entropy to decrease, as it would require a decrease in disorder and an increase in order, which goes against the natural tendency of systems to become more disordered over time.

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