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.

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134874371

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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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Use standard enthalpies of formation to calculate the standard change in enthalpy for the melting of ice. (The ΔH°_f for H₂O(s) is –291.8 kJ/mol.) Use this value to calculate the mass of ice required to cool 355 mL of a beverage from room temperature (25.0 °C) to 0.0 °C. Assume that the specific heat capacity and density of the beverage are the same as those of water.

Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the equation: CO₂(s) → CO₂(g) ◀ When carbon dioxide sublimes, the gaseous CO₂ is cold enough to cause water vapor in the air to condense, forming fog. When dry ice is added to warm water, heat from the water causes the dry ice to sublime more quickly. The evaporating carbon dioxide produces a dense fog often used to create special effects. In a simple dry ice fog machine, dry ice is added to warm water in a Styrofoam cooler. The dry ice produces fog until it evaporates away, or until the water gets too cold to sublime the dry ice quickly enough. Suppose that a small Styrofoam cooler holds 15.0 L of water heated to 85 °C. Use standard enthalpies of formation to calculate the change in enthalpy for dry ice sublimation, and calculate the mass of dry ice that should be added to the water so that the dry ice completely sublimes away when the water reaches 25 °C. Assume no heat loss to the surroundings. (The ΔH°_f for CO₂(s) is –427.4 kJ/mol.)

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Textbook Question

Use standard enthalpies of formation to calculate the standard change in enthalpy for the melting of ice. (The ΔH°_f for H₂O(s) is –291.8 kJ/mol.)

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In a sunny location, sunlight has a power density of about 1 kW/m². Photovoltaic solar cells can convert this power into electricity with 15% efficiency. If a typical home uses 385 kWh of electricity per month, how many square meters of solar cells are required to meet its energy requirements? Assume that electricity can be generated from the sunlight for 8 hours per day.

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Textbook Question

The kinetic energy of a rolling billiard ball is given by KE = 1/2 mv². Suppose a 0.17-kg billiard ball is rolling down a pool table with an initial speed of 4.5 m/s. As it travels, it loses some of its energy as heat. The ball slows down to 3.8 m/s and then collides head-on with a second billiard ball of equal mass. The first billiard ball completely stops and the second one rolls away with a velocity of 3.8 m/s. Assume the first billiard ball is the system. Calculate q.

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