A 100-W lightbulb is placed in a cylinder equipped with a moveable piston. The lightbulb is turned on for 0.015 hour, and the assembly expands from an initial volume of 0.85 L to a final volume of 5.88 L against an external pressure of 1.0 atm. Use the wattage of the lightbulb and the time it is on to calculate ΔE in joules (assume that the cylinder and lightbulb assembly is the system and assume two significant figures). Calculate w. Calculate q.

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Convert the time the lightbulb is on from hours to seconds by multiplying 0.015 hours by 3600 seconds/hour.

Calculate the energy supplied by the lightbulb in joules using the formula: \( q = \text{power} \times \text{time} \), where power is 100 W and time is the converted time in seconds.

Calculate the work done by the system using the formula: \( w = -P_{\text{ext}} \times \Delta V \), where \( P_{\text{ext}} \) is the external pressure (1.0 atm) and \( \Delta V \) is the change in volume (final volume - initial volume). Convert the work from L·atm to joules using the conversion factor 1 L·atm = 101.3 J.

Determine the change in internal energy, \( \Delta E \), using the first law of thermodynamics: \( \Delta E = q + w \).

Ensure that all values are reported with two significant figures, as specified in the problem statement.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 this question, the energy supplied by the lightbulb contributes to the internal energy of the system, which is related to the work done by the system and the heat exchanged with the surroundings.

Work (w)

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For a gas expanding against an external pressure, work can be calculated using the formula w = -P_ext ΔV, where P_ext is the external pressure and ΔV is the change in volume. The negative sign indicates that work is done by the system when it expands.

Heat (q)

Heat (q) refers to the energy transferred between the system and its surroundings due to a temperature difference. In this scenario, the heat absorbed or released by the system can be determined using the relationship ΔE = q + w, where ΔE is the change in internal energy. Understanding how to calculate q is essential for analyzing energy changes in the system.

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