The energy stored in a 52.0-μF capacitor is used to melt a 6.00 -mg sample of lead. To what volt

step 1 In this question, we are given that the energy stored in a 52 micro -farrant capacitor is used t

The energy stored in a 52.0-μF capacitor is used to melt a...

The energy stored in a $52.0-\mu \mathrm{F}$ capacitor is used to melt a $6.00$ -mg sample of lead. To what voltage must the capacitor be initially charged, assuming the initial temperature of the lead is $20.0^{\circ} \mathrm{C}$ ? Lead has a specific heat of $128 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$, a melting point of $327.3^{\circ} \mathrm{C}$, and a latent heat of fusion of $24.5 \mathrm{~kJ} / \mathrm{kg}$

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Key Concepts

Capacitor Energy Storage

This concept deals with the energy stored in a capacitor, typically given by the formula (1/2)CV², where C is the capacitance and V is the voltage. It illustrates how electrical energy can be stored and later discharged, which is fundamental in circuits and energy transfer systems.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates how much energy is needed to raise the temperature of a unit mass by one degree Celsius. It is essential for calculating the energy required to change the temperature of a substance without a phase change.

Latent Heat of Fusion

Latent heat of fusion refers to the energy required to change a substance from solid to liquid at its melting point without changing its temperature. This concept is key when dealing with phase changes and understanding how energy is absorbed during the melting of materials.

Energy Conversion in Thermal Processes

This concept involves the conversion of energy from one form to another, such as electrical energy stored in a capacitor being converted to thermal energy that raises the temperature and causes a phase change in a material. It relies on the principles of energy conservation, ensuring that the energy supplied matches the energy required for both temperature increase and phase transition.

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