AS0-cm-long 2-m-dameer clectric restance wie bergd in water is sed to determine the boiling heat tra fer coefficient in waterat 1stm experimentally The wire tem- peratore s measured to be 130 Cwhen the clectric power consamed to be 4.1 EW Uing Newto’ wof cooling, determine the boiling heat trfer co a wmeter ndate
The Correct Answer and Explanation is :
To determine the boiling heat transfer coefficient of water using an electrically heated wire, we can apply Newton’s law of cooling, which relates the heat transfer rate to the temperature difference between the wire and the surrounding water. The formula is:
[ Q = h \cdot A \cdot (T_{\text{wire}} – T_{\text{water}}) ]
Where:
- ( Q ) is the heat transfer rate (W)
- ( h ) is the heat transfer coefficient (W/m²·K)
- ( A ) is the surface area of the wire (m²)
- ( T_{\text{wire}} ) is the temperature of the wire (°C)
- ( T_{\text{water}} ) is the temperature of the water (°C)
Given Data:
- Wire length: 2 m
- Wire diameter: 0.1 cm (0.001 m)
- Wire temperature: 130°C
- Water temperature: 100°C
- Electrical power consumed: 4.1 W
Calculations:
- Surface Area of the Wire:
The surface area ( A ) of a cylinder is given by: [ A = \pi \cdot d \cdot L ] Substituting the given values: [ A = \pi \cdot 0.001\,\text{m} \cdot 2\,\text{m} \approx 0.00628\,\text{m}^2 ] - Heat Transfer Rate:
The heat transfer rate ( Q ) is equal to the electrical power consumed: [ Q = 4.1\,\text{W} ] - Temperature Difference:
[ \Delta T = T_{\text{wire}} – T_{\text{water}} = 130\,\text{°C} – 100\,\text{°C} = 30\,\text{°C} ] - Heat Transfer Coefficient:
Rearranging Newton’s law of cooling to solve for ( h ): [ h = \frac{Q}{A \cdot \Delta T} ] Substituting the known values: [ h = \frac{4.1\,\text{W}}{0.00628\,\text{m}^2 \cdot 30\,\text{°C}} \approx 21.8\,\text{W/m}^2\cdot\text{K} ]
Conclusion:
The boiling heat transfer coefficient of water, based on the given experimental setup, is approximately 21.8 W/m²·K.
Explanation:
In this experiment, an electrically heated wire dissipates heat into the surrounding water. The heat transfer rate is determined by the electrical power consumed by the wire, which is entirely converted into heat. The surface area of the wire is calculated based on its length and diameter, and the temperature difference between the wire and the water is used to determine the heat transfer coefficient. This coefficient quantifies the efficiency of heat transfer from the wire to the water, which is essential for understanding and optimizing boiling heat transfer processes.
It’s important to note that the heat transfer coefficient can vary depending on factors such as the wire’s surface condition, the presence of any coatings, and the flow characteristics of the water. Additionally, the boiling heat transfer coefficient is typically higher than that for single-phase heat transfer due to the latent heat involved in phase change during boiling.
For more detailed information on boiling heat transfer coefficients and their estimation, refer to the Big Chemical Encyclopedia.