If a 100 mL glass beaker is filled to the brim with ethyl alcohol at a temperature of 5.20°C, how much will overflow (in mL) when the alcohol's temperature reaches the room temperature of 20.0°C? (Assume the beaker is initially at room temperature.) mL How much less water (in mL) would overflow under the same conditions? mL
Energy transfer
The flow of energy from one region to another region is referred to as energy transfer. Since energy is quantitative; it must be transferred to a body or a material to work or to heat the system.
Molar Specific Heat
Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K-1)
Thermal Properties of Matter
Thermal energy is described as one of the form of heat energy which flows from one body of higher temperature to the other with the lower temperature when these two bodies are placed in contact to each other. Heat is described as the form of energy which is transferred between the two systems or in between the systems and their surrounding by the virtue of difference in temperature. Calorimetry is that branch of science which helps in measuring the changes which are taking place in the heat energy of a given body.
![### Thermodynamics and Fluid Expansion Problem
This section involves understanding the thermal expansion of liquids when subjected to temperature changes. Below are two related problems involving a glass beaker and two different liquids: ethyl alcohol and water.
#### Problem (a)
**Statement:**
If a 100 mL glass beaker is filled to the brim with ethyl alcohol at a temperature of 5.20°C, how much will overflow (in mL) when the alcohol's temperature reaches the room temperature of 20.0°C? (Assume the beaker is initially at room temperature.)
**Answer:**
```
______ mL
```
#### Problem (b)
**Statement:**
How much less water (in mL) would overflow under the same conditions?
**Answer:**
```
______ mL
```
---
### Explanation
In this exercise, we need to calculate the volume overflow when a liquid expands due to heating. When a liquid is heated, its volume increases due to thermal expansion. The amount of overflow can be determined using the formula for volumetric thermal expansion:
\[ \Delta V = V_0 \beta \Delta T \]
where:
- \(\Delta V\) is the change in volume.
- \(V_0\) is the initial volume.
- \(\beta\) is the coefficient of volumetric expansion of the liquid.
- \(\Delta T\) is the change in temperature.
**Given:**
- \(V_0\) for the beaker = 100 mL.
- Initial temperature \(T_i\) = 5.20°C.
- Final temperature \(T_f\) = 20.0°C.
- Change in temperature \(\Delta T = T_f - T_i = 20.0 - 5.20 = 14.80\)°C.
To solve each part, find the \(\beta\) value for ethyl alcohol and water, then calculate their respective \(\Delta V\). Finally, the difference between the volumes of overflow will answer part (b).
**Note:** The values for \(\beta\) are:
- Ethyl alcohol: \(\beta \approx 1.12 \times 10^{-3} \text{°C}^{-1}\)
- Water: \(\beta \approx 0.21 \times 10^{-3} \text{°C}^{-1}\)
These calculations would elucidate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5362cbea-9427-4b2b-99cb-57a208edd853%2F1aae277a-b9cc-4960-ba70-090e0e625acf%2Fky004w.png&w=3840&q=75)
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