As a balloon filled with an ideal gas rises and expands due to decreasing atmospheric pressure, it does work on its surroundings. Based on the first law of thermodynamics, what happens to its internal energy and temperature?

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BlackTom AI · Accepted Answer

The scenario involves a balloon with an ideal gas that expands as it rises and the external pressure decreases, doing work on its surroundings. According to the first law of thermodynamics, ΔU = Q − W, where W is the work done by the system. If we assume no heat is exchanged with the surroundings (Q = 0), the internal energy change equals −W, which means U decreases when the gas does work.

Option 1: 'Its internal energy and temperature will decrease because the balloon does work on the surroundings without receiving heat.' This aligns with the first law under the no-heat-transfer assumption: the system loses internal energy to perform expansion work, and for an ideal gas, U ∝ T, so temperature also falls. This option correctly captures both aspects.

Option 2: 'Its internal energy and temperature will increase because the volume of the balloon increases.' Although the volume increases, the expansion work reduces internal energy (with Q ≈ 0), so U and T do not increase. The increase in volume does not by itself imply a rise in internal energy for an ideal gas under these conditions.

Option 3: 'Its internal energy and temperature will remain constant because the expansion is balanced by the loss of pressure.' The idea of a balance with decreasing external pressure does not provide a mechanism to keep U constant. Without heat input, the work done during expansion lowers internal energy, so constant U is not correct.

Option 4: 'Its internal energy and temperature will increase because the balloon gains potential energy as it rises.' Gaining gravitational potential energy is a separate energy form and does not directly increase the internal energy of the gas. Energy accounting for the balloon involves U, W, and Q; rising to a higher altitude does not transfer energy into molecular internal energy in this context, so this option is misleading.

In summary, the most consistent choice with the first law and the behavior of an ideal gas undergoing expansion with negligible heat transfer is that the internal energy and temperature decrease.

Math & Science Prep Program Placement Assessment

As a balloon filled with an ideal gas rises and expands due to decreasing atmospheric pressure, it does work on its surroundings. Based on the first law of thermodynamics, what happens to its internal energy and temperature?

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