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A balloon is inflated from a volume of 0.112 L to 1.860 L against an external pressure of

0.987 atm. If the balloon also absorbs 125 J of heat, what is the change in internal energy (in J) for the inflation?

User Xorty
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1 Answer

4 votes

Answer: -49.8 J

Step-by-step explanation:

The first law of thermodynamics states that ΔU = q + w where ΔU is the internal energy of a system, q is the energy being transferred in or out of the system (positive if energy is transferred into the system, negative if transferred out), and w is work done on the system (positive if work is done on the system, negative if system is doing work on surroundings).

Finding w (work)

In order to find work, we use the formula for work, w = -P*ΔV, where P is the pressure of the surroundings and ΔV is the change in volume of the system.

In this problem, ΔV is 1.860-0.112 = +1.748 L and P is 0.987 atm, therefore

w = -0.987*1.748 = -1.725 L atm

Making units the same!

We are given q in joules, and the answer should be in joules, so we now convert L atm to joules. There are 101.325 joules in 1 L atm, so

-1.725 L atm * 101.325 J/1 L atm = -174.814 J = w

Note: You can also convert to joules by converting atm to Pa, pascals, and liters to m³.

Since work is negative, that means that the system is doing work on the surroundings. This makes sense, as inflating the balloon would do work on the surroundings. If we deflated the balloon, then the surroundings would be doing work on the system.

Plugging into the equation

Since the balloon absorbs 125 J of heat, q = 125 J. The sign is positive since energy is being transferred into the system.

Back to the equation, ΔU = q + w. We know q and w now, so we just have to add them to find the change in internal energy.

ΔU = 125 + -174.814 = -49.8 J

User Igor Semenov
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