A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:

Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (a) In which case does the gas have the higher temperature after addition of the electrical energy?

검증된 단계별 안내

Step 1: Understand the two scenarios: (1) the piston is allowed to move, and (2) the piston is fixed.

Step 2: Recall the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (q) minus the work done by the system (w): ΔU = q - w.

Step 3: In case (1), where the piston is allowed to move, the gas does work on the surroundings as it expands. Therefore, some of the added energy is used to do work, and less energy is available to increase the temperature of the gas.

Step 4: In case (2), where the piston is fixed, no work is done by the gas because the volume does not change. All the added energy goes into increasing the internal energy of the gas, which results in a higher temperature.

Step 5: Conclude that the gas will have a higher temperature in case (2) where the piston is fixed, as all the added energy is used to increase the internal energy and temperature of the gas.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the gas in the cylinder, the energy added by the heater (100 J) will either increase the internal energy of the gas or do work on the piston, depending on whether the piston is allowed to move or is fixed.

Work Done by a Gas

When a gas expands against a piston, it does work on the piston, which can affect its temperature. In case (1), where the piston can move, some of the energy added will be used to do work, resulting in a lower temperature increase compared to case (2), where the piston is fixed and all the energy contributes to increasing the internal energy and temperature of the gas.

Temperature and Internal Energy

Temperature is a measure of the average kinetic energy of the particles in a substance. In thermodynamics, when energy is added to a gas, its internal energy increases, which typically raises its temperature. In the fixed piston scenario, all the added energy increases the internal energy, leading to a higher temperature than in the moving piston scenario, where some energy is used for work.