You hold an inflated balloon over a hot air vent in your house and watch it slowly expand. You then remove it and let it cool back to room temperature. During the expansion, which was larger: the heat added to the balloon or the work done by the air inside? explain. (assume that air is an idea gas.) Once the balloon has returned to room temperature, how does the net heat gained or lost by the air inside it compare to the net work done on it by the surrounding air?
The answer is 12.1 seconds
To determine which was larger during the expansion, the heat added to the balloon or the work done by the air inside, we need to analyze the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In equation form, it can be expressed as:
ΔU = Q - W
Where:
ΔU = change in internal energy
Q = heat added to the system
W = work done by the system
During the expansion of the balloon over the hot air vent, heat is transferred from the hot air vent to the balloon. Heat transfer occurs because the temperature of the air inside the balloon increases due to the hot air from the vent. This means that Q, the heat added to the balloon, is positive.
Simultaneously, the air inside the balloon is doing work by pushing against the elastic walls of the balloon as it expands. Work done by a gas can be calculated using the equation:
W = PΔV
Where:
P = pressure of the gas
ΔV = change in volume of the gas
Since the balloon is expanding against atmospheric pressure, which remains constant, the work done by the air inside the balloon can be considered as the pressure times the change in volume. As the gas expands, the volume increases, and so does the work done. This implies that W, the work done by the air inside the balloon, is also positive.
Now, comparing the heat added (Q) and the work done (W), both values are positive, indicating that energy is being added to the system during the expansion. However, it is challenging to determine which one is larger without specific values or conditions.
Once the balloon returns to room temperature, the net heat gained or lost by the air inside will depend on the heat transfer between the air inside the balloon and its surroundings. If the temperature of the surroundings is lower than the temperature of the air inside the balloon, then heat will be lost by the air inside the balloon. Conversely, if the surroundings are warmer, heat will be gained by the air inside.
The comparison between the net heat gained or lost and the net work done on the balloon by the surrounding air follows the same principles discussed earlier. The first law of thermodynamics can be applied to calculate the change in internal energy (ΔU), which will be the net heat added or lost minus the net work done. However, in this case, we would need more information regarding the specific conditions and values to determine the exact relationship between the two.