You add equal amounts of heat to two identical cylinders containing equal amounts – [Free] B62
You add equal amounts of heat to two identical cylinders containing equal amounts of the same ideal gas. Cylinder A is allowed to expand, while cylinder B is not. Part A How do the temperature changes of the two cylinders compare? Cylinder B will experience a greater temperature change. Cylinder A will experience a greater temperature change. The two cylinders will experience the same temperature change.
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Answer
🔥 Temperature Change in Two Cylinders of Ideal Gas
Question
Cylinder A is allowed to expand, while Cylinder B is not.
Part A: How do the temperature changes of the two cylinders compare?
Options:
- Cylinder A will experience a greater temperature change.
- Cylinder B will experience a greater temperature change.
- The two cylinders will experience the same temperature change.
Answer
✅ To solve this, we analyze the energy changes in both cylinders using the first law of thermodynamics:
where:
- ΔU = change in internal energy
- Q = heat added
- W = work done by the gas
🌟 Cylinder B (Constant Volume)
Since the volume does not change, no work is done (W = 0), so:
All the heat added increases the internal energy and therefore the temperature. The temperature change in Cylinder B can be expressed as:
where n is the number of moles and C_V is the molar heat capacity at constant volume.
🌟 Cylinder A (Expands)
When the gas is allowed to expand, it does work on its surroundings (W > 0), so:
Here, part of the heat is used to do work, leaving less energy to increase internal energy and temperature:
🔷 Comparison
Since W > 0 for Cylinder A, it follows that:
Therefore, Cylinder B (which does not expand) will experience a greater temperature change because all the heat goes into increasing internal energy without doing work.
✨ Final Answer:
Cylinder B will experience a greater temperature change.