Question

The Atmos clock (the so-called perpetual motion clock) gets its name from the fact that it runs off pressure variations in the atmosphere, which drive a bellows containing a mixture of gas and liquid ethyl chloride. Because the power to drive these clocks is so limited, they have to be very efficient. In fact, a single \(60.0\)-W lightbulb could power 240 million Atmos clocks simultaneously. Find the amount of energy, in joules, required to run an Atmos clock for 1 day.

Short answer

The energy required to run an Atmos clock for 1 day is 0.0216 joules.

Step-by-step solution

Identify the Problem Parameters

First, we note that the problem provides us with the power of a single lightbulb, which is 60 watts, and the number of Atmos clocks it can power simultaneously, which is 240 million. We need to figure out how much energy in joules is required to run one Atmos clock for 1 day.

Calculate Power for One Atmos Clock

The power required for one Atmos clock can be calculated by dividing the power of the lightbulb by the number of Atmos clocks it can power:\[ \text{Power per Atmos clock} = \frac{60 \, \text{W}}{240,000,000} = 2.5 \times 10^{-7} \, \text{W} \]

Convert Power to Energy for One Day

To convert power (in watts) to energy (in joules), we need to multiply by the time the clock runs, which is 1 day. Since 1 day = 24 hours = 86400 seconds, the energy for 1 day is calculated as:\[ \text{Energy} = \text{Power} \times \text{Time} = 2.5 \times 10^{-7} \, \text{W} \times 86400 \, \text{s} \]

Calculate Energy in Joules

Perform the multiplication to find the energy:\[\text{Energy} = 2.5 \times 10^{-7} \, \text{W} \times 86400 \, \text{s} = 0.0216 \, \text{J} \]

Conclusion

The amount of energy required to run an Atmos clock for 1 day is \(0.0216\) joules.

Key concepts

Energy Conversion

Energy conversion is a fundamental concept in physics. It refers to the transformation of energy from one form to another. In the case of the Atmos clock, energy conversion occurs as it utilizes atmospheric pressure variations to drive its mechanisms. These variations are captured by a bellows system containing a specific gas and liquid mixture.

The efficiency of energy conversion in such systems is vital because of the limited energy sources available to them. For the Atmos clock, even the smallest amount of mechanical energy harvested from the environment can keep it running smoothly. This is because it converts the subtle changes in atmospheric pressure directly into mechanical energy without significant wastage.

• This means that instead of pulling power from an electrical source like a typical watch battery, the Atmos operates with ambient energy.
• This innovative approach allows the Atmos clock to mimic the elusive concept of perpetual motion, since it continuously utilizes energy from its surroundings without external input beyond atmospheric changes.

Understanding energy conversion mechanics gives insight into how such devices offer sustainable and efficient timekeeping solutions.

Efficiency

Efficiency in mechanical or energy systems indicates how well energy input is converted into useful work output. Higher efficiency implies less energy wastage, which is crucial for devices like the Atmos clock.

Atmos clocks demonstrate impressive efficiency. A standard 60-watt lightbulb can power up to 240 million Atmos clocks. This amazing fact underscores the clock's ability to use minimal energy effectively. In simple terms, these clocks waste very little of the ambient energy they draw in.

This efficiency is achieved through meticulous design and engineering, ensuring that moving parts are optimized and friction minimized.

• Such efficiency means these clocks require very little additional power to maintain their operation once started.
• The result is a clock that can operate almost indefinitely, provided there are natural pressure variations, achieving near-perpetual motion through remarkable efficiency.

By focusing on energy conversion and minimization of energy loss, Atmos clocks set a benchmark for high-efficiency devices, exploring new potentials for sustainability.

Joules

The joule is the unit of energy in the International System of Units (SI). It quantifies the amount of work done when a force is applied, or energy is transferred. For the Atmos clock, energy in joules is a small amount, showing how little energy is needed for its daily operation.

The calculation for how much energy it takes to run an Atmos clock for one day shows this clearly. When converting power to energy, the result is only 0.0216 joules for a day. This conversion involves determining how many seconds a day contains, 86,400, and using the power used by a single clock in watts.

With such a minuscule amount of joules needed, the Atmos clock is a marvellous showcase of efficiency and minimal energy requirement.

• Knowing the energy needed in joules highlights the possibility of designing devices that draw power from unlikely ambient sources.
• It reveals the potential advancements in engineering to achieve high functionality from low energy consumption.

The concept of joules thereby not only measures energy but also challenges engineers to design highly efficient, resource-light technologies like the Atmos clock.