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An instrumentation transmitter pod is a box containing electronic circuitry and a power supply for sending sensor signals to a base receiver for recording. Such a pod is placed on a conveyor system, which passes through a large vacuum brazing furnace as shown in the sketch. The exposed surfaces of the pod have a special diffuse, opaque coating with spectral emissivity as shown. To stabilize the temperature of the pod and prevent overheating of the electronics, the inner surface of the pod is surrounded by a layer of a phase- change material (PCM) having a fusion temperature of \(87^{\circ} \mathrm{C}\) and a heat of fusion of \(25 \mathrm{~kJ} / \mathrm{kg}\). The pod has an exposed surface area of \(0.040 \mathrm{~m}^{2}\) and the mass of the PCM is \(1.6 \mathrm{~kg}\). Furthermore, it is known that the power dissipated by the electronics is \(50 \mathrm{~W}\). Consider the situation when the pod enters the furnace at a uniform temperature of \(87^{\circ} \mathrm{C}\) and all the \(\mathrm{PCM}\) is in the solid state. How long will it take before all the PCM changes to the liquid state?

Step by step solution

01

Identify the energy input to the PCM

The energy input to the PCM comes from the electronic power dissipation inside the pod. We are given this value as \(50 \mathrm{~W}\).

02

Calculate the energy needed for the phase change of PCM

The energy needed to change the phase of the PCM can be calculated using the formula: Energy needed = mass (PCM) \(\times\) heat of fusion Where: mass (PCM) = \(1.6 \mathrm{~kg}\) heat of fusion = \(25 \mathrm{~kJ} / \mathrm{kg}\) Now we need to convert the heat of fusion from \(\mathrm{kJ}\) to \(\mathrm{J}\): heat of fusion = \(25 \mathrm{~kJ/kg} \times 1000 \mathrm{~J/ kJ} = 25000 \mathrm{~J/kg}\) Therefore, the energy needed is: Energy needed = \(1.6 \mathrm{~kg} \times 25000 \mathrm{~J/kg} = 40000 \mathrm{~J}\)

03

Apply the energy conservation concept

Now we will use the energy conservation concept to find the time necessary for the phase change: Energy input = Energy needed Since energy is power multiplied by time, we can write: Power (electronics) \(\times\) time = Energy needed

04

Calculate the time for the phase change

Now, we will calculate the time necessary for the phase change: \(\text{time} = \frac{\text{Energy needed}}{\text{Power (electronics)}}\) Where: Energy needed = \(40000~\text{J}\) Power (electronics) = \(50 \mathrm{~W}\) So, the time required is: \(\text{time} = \frac{40000 \mathrm{~J}}{50 \mathrm{~W}} = 800 \mathrm{~s}\) Thus, it will take 800 seconds for all the PCM to change from the solid state to the liquid state.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Conservation

Energy conservation is a fundamental principle that governs the behavior of energy in any system. The essence of energy conservation is that energy cannot be created or destroyed; it can only be transferred from one form to another. In the context of phase change materials (PCMs), this principle is vital for understanding how energy is managed and utilized.

PCMs store and release energy through phase changes, such as from solid to liquid or liquid to gas. The energy absorbed during this process is known as the "heat of fusion". When considering a system like the instrumentation transmitter pod, we need to estimate how long it will take for the PCM to absorb enough energy to change state fully.

The calculation involves quantifying the energy input (in this case, from the electronics power dissipation) and matching it to the energy required for the phase change. This approach allows us to predict the time required for a complete phase change, demonstrating energy conservation's role in thermal management strategies.

Heat of Fusion

The heat of fusion is a material property that indicates the amount of energy required to change a unit mass of a solid to a liquid at a constant temperature. It's a key concept for understanding how phase change materials help in energy regulation, especially in thermal management systems.

To find the heat required for a phase change, we multiply the mass of the PCM by its heat of fusion. This calculation indicates the total energy needed for the entire phase change process. For example, if the PCM has a heat of fusion of 25 kJ/kg and a mass of 1.6 kg, the energy needed becomes:

• Converted to joules: Heat of fusion = 25 kJ/kg x 1000 J/kJ = 25000 J/kg
• Total energy needed = 1.6 kg x 25000 J/kg = 40000 J

By determining these values, we can effectively use PCMs in applications that require precise thermal control, ensuring devices like transmitter pods operate efficiently within their specified temperature ranges.

Thermal Management

Thermal management is the process of controlling and regulating the temperature of a device to ensure its functionality and longevity. In electronic applications, like the instrumentation transmitter pod, avoiding overheating is crucial.

Phase change materials play an essential role in thermal management by absorbing excess heat and stabilizing temperatures. The fusion process, where PCMs absorb heat without a significant temperature increase, allows devices to maintain safe operating conditions. This is particularly useful in environments with fluctuating temperatures or high thermal loads.

The heat absorbed by the PCM helps delay temperature rises that could damage sensitive electronic components. Additionally, when the environment cools, the PCM can revert to its solid state, releasing stored energy and providing consistent thermal management.

By incorporating PCMs into thermal management systems, we leverage their latent heat properties to protect electronics, improve energy efficiency, and enhance the overall reliability of devices.