In the fourth installment of our series of espresso coffee thermal analyses, we will examine what happens when evaporation and convection losses are minimized. In past blogs we measured the temperature of the espresso cups and espresso coffee with the liquid exposed to the ambient air. This causes the coffee to lose thermal energy in two ways. The first is through convection heat transfer. Convection takes place when thermal energy is passed through a medium such as air and water. This is different then conduction which occurs when thermal energy is passed through direct contact. The coffee also loss thermal energy through evaporation. Evaporation is an endothermic process, meaning that as it takes place the thermal energy is absorbed. Even in a liquid that is not at its boiling temperature, some molecules have enough energy to evaporate and therefore remove energy from the liquid. When these two processes combine, they remove a large amount of thermal energy from the espresso coffee, as seen in the previous blogs. This means that if the effects of evaporation and convection are minimized the espresso coffee should stay warmer for longer.

**Thermal Management Experiment**

**Purpose**

The purpose of this experiment is to evaluate the impact on thermal energy loss that covering a ceramic espresso cup will have on its long term temperature. Simply, how much warmer will a covered ceramic espresso cup be when compared to an uncovered ceramic espresso cup?

**Scope**

The scope of this experiment is to create an espresso coffee with maximum heat retention using a covered ceramic espresso cup. The ceramic espresso cup will be covered with a ceramic saucer turned upside down. Each temperature will be measured using an Omega TM HH806AU J-type thermocouple reader. We will preheat the ceramic espresso cup with hot water and then fill it with three ounces of espresso coffee while recording the temperature of the espresso coffee over time.

**Procedure**

The basic procedure for the experiment will be as follows:

- Measure the height at which the ceramic espresso cup holds 3 ounces.
- Fill the ceramic espresso cup with hot water and record temperatures for 2 ½ minutes.
- Compress espresso grinds into basket, filling basket about ¾ full.
- Run machine for 5 seconds, in order to wet the grinds which will help avoid “jetting”.
- Run machine until espresso coffee reaches the 3 ounce line, at this time collect the temperature of the ceramic espresso cup and of the espresso coffee.
- Continually measure temperature for the first three minutes that the espresso coffee is in the ceramic espresso cup.
- Collect temperature readings at 2 minute intervals for the next twenty minutes.

**Experimental Results of Ceramic Espresso Cup Preheating**

- The recorded starting temperature of the ceramic espresso cup before adding hot water was 26.5°C (79.7oF).
- The ceramic espresso cup rose steadily in temperature to 48.9°C (120oF) in 124 seconds before flattening out for the rest of the measurement.
- As seen in Figure 1 below, in 45 seconds the ceramic espresso cup reached a temperature of 40°C (104oF). This is 85% of the maximum temperature but in less than half of the time.

*Figure 1:Preheating of Ceramic Espresso Cup with Hot Water*

- The ceramic espresso cup reached a peak temperature of 49.9°C (121.9oF) in 150 seconds.
- To calculate the time constant, the time it takes to reach 63.2% of the maximum value, the equation below was used:

T^{o}*(e-t/τ) Eqn. 1

where T^{o} is the initial temperature, e is Euler’s constant, t is the time and τ is the time constant, and was calculated to be 77.

- The change in the temperature of the hot water from its maximum (77.7°C,171.9oF) at time zero and its minimum (67.8°C,154.1oF).

**Experimental Results of Covered Ceramic Espresso Cup with Espresso Coffee**

- When the espresso coffee was poured into the ceramic espresso cup, the espresso coffee was at a temperature of 79°C (174.2oF) and the cup was at a temperature of 27.6o (81.6oF).
- As can be seen in Figure 2 below, the ceramic espresso cup increased in temperature to a maximum temperature of 47.2°C (116.9oF).

*Figure 2: Temperature Readings from Covered Ceramic Espresso Cup with 3 ounces of Espresso Coffee*

- It is also seen in Figure 2 above, that the espresso coffee declined to a minimum temperature of 60.1°C (140.2oF).
- In Figure 3 below, it can be seen that the even though the covered and uncovered ceramic espresso cups started at roughly the same temperature, the uncovered cup cooled much quicker.

*Figure 3: Comparison of Cooling Between Covered and Uncovered Ceramic Espresso Cup*

- After 5 minutes of being in the ceramic espresso cup, we measured the covered espresso coffee to have a temperature of 58.6°C (137.4oF) and the uncovered espresso coffee to have a temperature of 59.4°C (139oF).
- After the espresso coffee had been in the uncovered ceramic espresso cup for 23 minutes we measured the temperature to be 41.7°C (107.1oF), a difference of 17.7°C (31.9oF).
- After the espresso coffee had been in the covered ceramic espresso cup for 23 minutes we measured the temperature to be 46.6°C (115.9oF), a difference of 12°C (21.5oF).

**Analysis of Preheating Ceramic Espresso Cup**

For the purposes of this analysis the specific heat of the ceramic espresso cup is assumed to be 1090 J/KgK, which is the specific heat of standard ceramic. The mass of the cup was calculated to be 553 g with a volume of 207.2 ml (7oz).

To calculate the maximum theoretical temperature that the ceramic espresso cup could be heated to, the equation below is used.

c^{cup}*m^{cup}*ΔT^{cup}= c^{water}*m^{water}*ΔT^{water}= Q Eqn. 2

where Q is the thermal energy, c is the specific heat, m is the mass and ΔT is the change in temperature. This relationship yields a theoretical maximum temperature of 55.7°C (132.3oF). Similar to past weeks this theoretical temperature is not attainable due to convective losses and evaporation. Even though this experiment is looking to avoid convective losses and evaporation, in the preheating phase it needs to remain the same as past weeks for comparison purposes.

**Analysis of Covered Ceramic Espresso Cup with Espresso Coffee**

As seen in Figure 3, the covered ceramic cup kept the espresso coffee much warmer over time than the uncovered ceramic cup. After 23 minutes the temperature in the uncovered ceramic espresso cup was 4.9°C (8.8oF) cooler than in the covered ceramic cup. The cover on the cup is responsible for this temperature change because it trapped a majority of the convective heat loss and evaporation. However, cover does not perfectly manage the thermal energy from the espresso coffee because the cover was ceramic and absorbed some of the convective thermal energy, reaching a maximum temperature of 38.8°C (101.9oF).

**Conclusion**

After examining the results it may not seem as if the temperature difference between a covered and uncovered ceramic espresso cups warrants a major change in future espresso coffee drinks. However, the important result from this experiment is that a “lid” does have a noticeable impact on the temperature of the drink contained within. The results from this experiment can be applied to any drink that is supposed to be warm for a lengthy period of time. After four weeks of espresso coffee experiments, we are one step closer to creating the perfectly heated cup of espresso.1212

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