# Introduction to Thermal Analysis of an Insulated Bodum™ Espresso Cup

In the second thermal analysis of espresso coffee cup materials we will be examining another type of espresso cup which was overlooked in the previous experiment. This cup is known as an insulated espresso cup. Unlike the paper, Styrofoam and ceramic espresso cups from the previous week’s experiment, a Bodum™ insulated espresso cup comprises two layers of glass separated by a small chamber of air. Air has a specific heat capacity of just 1.005 kJ/kg·K and a thermal conductivity of .024 W/m·K. Due to its low thermal conductivity heat transfer will occur at a slow rate through the glass.

**Purpose**

The purpose of this experiment is to understand the material properties of a Bodum ™ insulated espresso cup and its ability to help the espresso coffee retain its thermal energy. Simply, how much hotter is espresso coffee in the Bodum™ insulated espresso cup when compared to cups of other materials tested in the previous experiment.

**Scope**

The scope of this experiment is to create an espresso coffee with maximum heat retention using a Bodum™ insulated espresso cup. Each temperature will be measured using an Omega™ HH806AU J-type thermocouple reader. We will preheat the Bodum™ insulated 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 is as follows:

- Measure the height at which each Bodum™ insulated espresso espresso cup holds 3 ounces.
- Fill the Bodum™ insulated espresso cup with hot water and record temperatures for 2.5 minutes.
- Compress espresso grinds into basket, filling basket about 75% full.
- Run machine until the water contacts the coffe and the tone of the pump changes, then immediately turn off the water pump. This is in order to wet the grinds and allow them to expand before brewing, which will help avoid “jetting”.
- Run machine until espresso coffee reaches the 3 ounce line, at this time collect the temperature of the cup and of the coffee as the espresso comes out.
- Continually measure temperature for the first three minutes that the espresso coffee is in each cup.
- Collect temperature readings at 2 minute intervals for the next 20 minutes.

**Experimental Results of Bodum™ Insulated Espresso Cup Preheating**

- The measured starting temperature for the Bodum™ insulated espresso cup before adding hot water to it was 26.3°C (79.4°F).
- The temperature of the Bodum™ insulated espresso cup did not reach 32.2°C (90°F) until 90 seconds passed, as seen in Figure 1 below.

*Figure 1: Preheating of Bodum ™ Insulated Espresso Cup with Hot Water*

- At 45 seconds, when the hot water would normally be poured out, the measured temperature of the Bodo insulated espresso cup was 28.4°C (83.1°F).
- From the 45 second mark to the final time at 150 seconds (2.5 minutes) the Bodum™ insulated espresso cup rose another 7.1°C (12.8°F) to 35.5°C (95.9°F).
- The Bodum™ insulated espresso cup reached a peak temperature of 35.5°C (95.9°F) at 150 seconds, and based on the trend when the measurement finished, would have continued to rise.
- To find the time constant, the time it takes to reach 63.2% of the maximum value, the equation used is:

T^{o}*(e_{-t/τ}) Eqn. 1

where To is the initial temperature, e is Euler’s constant, t is the time and τ is the time constant, and was calculated to be 60.6.

- The change in the hot water temperature from its maximum (77.2°C, 170.9°F) at time zero and its minimum (70.4°C, 158.7°F) at 150 seconds was 6.8°C (12.2°F).

**Experimental Results of Bodum™ Insulated Espresso Cup with Espresso Coffee**

- When the espresso coffee was poured into the Bodum™ insulated espresso cup the coffee was at a temperature of 73.1°C (163.6°F) and the Bodum™ insulated espresso cup was at a temperature of 29.4°C (85°F).
- As can be seen in Figure 2 below, the Bodum™ insulated espresso cup temperature rose very slowly and reached a maximum temperature of just 35.8°C (96.5°F).

*Figure 2: Temperature Readings from Bodum™ Espresso Cup with 3 ounces of Espresso Coffee*

- It can also be seen in Figure 2 that the espresso coffee slowly declined in temperature, reaching a minimum of 64.9°C (148.8°F) at the end of the measurement.
- In Figure 3 below it can be seen that 20 minutes after the espresso coffee had been poured into the Bodum™ insulated espresso cup the temperature of the espresso coffee was still 48.3°C (119°F).

*Figure 3: Temperature Readings over an Extended Period of Time for Bodum™ Insulated Espresso Cup*

**Analysis of Preheating Bodum ™ Insulated Espresso Cup**

For the purpose of this analysis the specific heat of glass was found to be 0.84 KJ/Kg·K and the thermal conductivity was found to be 1.05 W/m·K. The mass of the cup was calculated to be 244.5 grams. In order to find the maximum theoretical temperature the following equation is used:

c^{Bodum} *m^{Bodum} *ΔT^{Bodum} = 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. By using this relationship the maximum theoretical temperature calculated to be possible was 55.6°C (132.1°F). This temperature is 77% of the maximum temperature of the water but is unreachable due to convection heat losses and evaporation.

**Analysis of Bodum™ Insulated Espresso Cup with Espresso Coffee**

As seen in Figure 3, the Bodum™ insulated espresso cup allowed the espresso coffee to cool extremely slowly compared to the cups tested in the previous experiment. The Styrofoam espresso cup from last week’s blog allowed the espresso coffee to cool by 33.9°C (61.1°F). The Bodum™ insulated espresso cup had a temperature difference of just 24.8°C (44.6°F) between its maximum temperature of 73.1°C (168.9°F) and its final temperature after 23 minutes, 48.3°C (119°F).

**Conclusion**

After examining the results from the Bodum™ insulated espresso cup experiment it is clearly evident that the Bodum™ insulated espresso cup was the most successful cup in terms of containing the heat energy of the espresso coffee. This can mainly be attributed to the air sealed within the cup which serves as an insulator. Based on this three week espresso coffee heat transfer experiment described in the last two blogs, Espresso Blog 2 and Espresso Blog 1, it is evident that if you want to keep your coffee as hot as possible for as long as possible, the Bodum™ insulated espresso cup is the best option.

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