**Thermal Analysis of Making Espresso Coffee**

In our blog this week, we will focus on aspects of the thermal engineering that produces a standard cup of espresso and one way to optimize the end result. Espresso, which is very similar to coffee, is essentially a thick beverage topped with dense light brown foam known as crema, comprised solely of coffee and water. The espresso machine forces the hot water through a small perforated metal basket which contains the compressed finely ground coffee beans. The engineering difference between an espresso machine and a standard slow drip coffee machine is that the espresso machines uses nine bars (130 PSIG) of atmospheric pressure and a sealed vessel to force water over the ground beans to create a higher concentrated beverage.

Espresso first gained popularity in the US among Italian immigrant communities and was then adopted by epicureans. However it didn’t truly became a common item on menus until the so-called “Second Wave of Coffee” which was brought on by the popularity of mega chain coffee shops. In order to sustain the temperature of the espresso once it is poured into the cup it will often be preheated. This is normally achieved by filling the cup with hot water and letting it acquire thermal energy for about thirty seconds. Some tea drinkers are persnickety about their tea preparation, and preheat their tea cup, their milk, and their tea pot. One often sees espresso cups kept on the top of large espresso machines. The purpose of this is to pre-warm the cup, so as not to excessively cool the espresso.

**Heat Transfer Experiment**

**Purpose**

The purpose of this experiment is to determine the preheating effect of hot water on a ceramic cup in the process of making an espresso coffee. Simply, how much hotter is the resulting coffee when the espresso cup is preheated.

**Scope**

The scope of this experiment is to create an espresso coffee with an optimized initial ceramic cup temperature achieved through a preheating phase utilizing hot water. Each temperature will be measured using an OmegaTM HH806AU J-type thermocouple. We will pour hot water in the empty espresso cup, and see how hot the cup becomes, and the resulting espresso temperature. We will compare this to espresso served in a cup that will not be preheated.

**Procedure**

The basic procedure for this experiment will be as follows:

- Ensure that ceramic espresso cup is at room temperature.
- Put espresso grinds into basket and compress, lock basket in place.
- Fill ceramic espresso cup with hot water to preheat ceramic espresso cup. Measure temperature change of the ceramic espresso cup and hot water over time, remove hot water.
- Run machine for 5 seconds to pre-wet the espresso grinds, in order to avoid jetting.
- Ensure temperature is acceptable, signaled by a green light, and run the espresso machine until the cup is about 28.58 mm (1 1/8 inches) full, this is about 3 ounces. This time collect the temperature of the ceramic espresso cup and of the espresso coffee in the cup.

We then repeated these steps with the exception of the preheating phase for comparison purposes.

**Experimental Results of Preheating the Ceramic Espresso Cup**

- We measured the starting temperature for the ceramic espresso cup in this scenario was to be 25.78°C (78.4°F).
- As can be seen in Figure 1, when introduced to the cup the hot water had a temperature of 71.89°C (161.4°F) and then decreased over time as the ceramic espresso cup increased.

Figure 1: Preheating of Ceramic Espresso Cup with Hot Water

- At 30 seconds, when the water would regularly be poured out, we measured the hot water to have a temperature of 62.61°C (144.7°F) and the ceramic cup to have a temperature of 40.33°C (104.6°F.)
- The ceramic espresso cup reached a peak temperature of 43.44°C (110.2°F) at 200 seconds, or 2 minute and 20 seconds. At this time the hot water had a temperature of 59.06°C (138.3°F).
- At the end of the experimental preheating phase, after 7 minutes and 28 seconds had elapsed, the ceramic espresso cup had a temperature of 39.78°C (103.6°F) and the hot water had a temperature of 56.17°C (133.1°F).
- The time constant, calculated by the equation

T^{o}*(e_{-t/tau}) Eqn. 1

where To is the initial temperature,e is Euler’s constant, t is the time and tau is the time constant is 69.66. This means that it takes 69.66 seconds to reach 63.2% of the maximum temperature.

- As can be seen in Figure 2, the espresso coffee remained at a fairly steady temperature with an average of 77.33°C (171.2°F).

Figure 2: Temperature of Espresso Coffee and Preheated Ceramic Espresso Cup

- The ceramic espresso cup was at a temperature of 38.5°C (101.3°F) when the espresso coffee first entered it and when the ceramic espresso cup was filled with espresso coffee, after 18 seconds, it had risen to 39.28°C (102.7°F).
- At the time the ceramic espresso cup would have been served the temperature of the espresso coffee was 74.11°C (165.4°F).

**Experimental Results of Non-preheated Ceramic Espresso Cup**

- We measured the starting temperature for the ceramic espresso cup in this scenario was to be 25.78°C (78.4°F).
- As can be seen in Figure 3 the espresso coffee started at a slightly lower temperature and declined rapidly when compared to the preheated ceramic espresso cup’s espresso coffee.

Figure 3: Temperature of Espresso Coffee and Non-Preheated Ceramic Espresso Cup

- The espresso coffee peaked at just 69.17°C (156.5°F) at a time of 2 seconds and declined steadily from there.

**Analysis of Preheating the Ceramic Espresso Cup**

For the analysis of this experiment we assumed the ceramic espresso cup to be 553 grams with a total volume of 207.02ml (7 ounces).

When the hot water is introduced to the ceramic cup there is a physical limit on how much it is able to preheat the ceramic. This is due to factors such as the volume of the ceramic espresso cup and the hot water and the specific heat of the ceramic espresso cup and the hot water. In this situation the maximum theoretical temperature that the ceramic espresso cup could have reached is 52.5°C (126.5°F). This is found using the relationship:

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

where Q is the thermal energy, c is the specific heat, m is the mass and ΔT is the change in temperature. The specific heat and mass of the ceramic espresso cup are in parenthesis because the exact mass of the cup was unknown and so the thermal mass was calculated using data collected. The theoretical temperature is not reached in the experiment due to convective losses and, in a small part, evaporation of the water. Due to the previous exchange of heat energy between the hot water and the ceramic espresso cup, the ceramic espresso cup will not absorb a large amount of heat energy from the espresso coffee when it is poured into the cup.

**Analysis of not Preheating the Ceramic Espresso Cup**

For the analysis of this experiment we assumed the ceramic espresso cup to be 553 grams with a total volume of 207.02ml (7 ounces). The espresso coffee had a volume of 88.72 (3 ounces). The ceramic espresso cup was assumed to have a specific heat of 1090 J/kg*K.

Using Eqn. 2 the maximum theoretical temperature that the non-preheated ceramic espresso cup can achieve is only 45.83°C (114.5°F). This leaves a gap of 5.7°C (12°F) between the ideal max temperatures simply because of preheating.

**Conclusion**

The first conclusion from this experiment is that preheating the ceramic espresso cup has a very large impact on the drinking temperature. With a preheated ceramic cup very little thermal energy was transferred from the espresso coffee to ceramic espresso cup, therefore resulting in a warmer espresso. When examining the differences in the trends of the two figures it can be seen that the hot water lost a great deal of heat energy while the espresso coffee did not. In the part of the experiment where the coffee was poured into the cup without a preheating phase there was an immediate difference. When the preheated ceramic espresso cup was filled the temperature of the coffee remained fairly constant at 76.67°C (170°F), however by the time the non-preheated ceramic espresso cup was filled the coffee was already below 71.11°C (160°F) and on the decline. The non-preheated ceramic espresso cup did not reach 37.78°C (100°F) until 54 seconds of having espresso coffee in it, while the preheated cup never dipped below 38.5°C (101.3°F). This means that the espresso coffee lost a good amount of thermal energy as it heated the ceramic espresso cup.

Second, the temperature of the cup will not continually rise with time if left out with hot water. As stated earlier, the standard preheating phase lasts about 30 seconds. However, when examining Figure 1 it can be seen that the maximum ceramic espresso cup temperature is achieved at 200 seconds, or 3 minutes and 20 seconds. The difference between this temperature (43.44°C, 110.2°F) and the temperature at 30 seconds (35.11°C, 95.2°F) is 8.33°C (20°F). However, the point of an espresso is to avoid waiting for a cup of coffee. When examining Figure 1 it can be seen that the temperature reaches 95% of the maximum temperature (40.33°C, 104.6°F) at 60 seconds and 90% of the maximum (37.33°C, 99.2°F) at 43 seconds. Instead of waiting for two minutes and twenty seconds, waiting in the range of 45 seconds to a minute can achieve a comparable result in much less time.

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