A cylindrical flask is being used as an insulator to store tea and keep it hot on a cold day. How will increasing the thickness by 4 times of all walls and halving the contact surface area (without changing the type of material the walls are made of) of the insulator affect the rate of heat loss?

Question

BlackTom AI · Accepted Answer

Fourier’s law of heat conduction gives the heat-loss rate through a wall as Q̇ = k A ΔT / d, so thicker walls or smaller contact area reduce heat flow.

1. Relevant knowledge points and concepts
- Steady-state conduction: Q̇ = k A ΔT / d, where k is thermal conductivity (material fixed), A is contact area, d is wall thickness, ΔT is temperature difference.
- Thermal resistance viewpoint: R = d/(kA). Increasing R lowers Q̇ since Q̇ = ΔT / R.

2. Complete reasoning process step by step
- Let initial thickness = d and initial area = A. Initial heat loss: Q̇_initial = k A ΔT / d.
- New thickness = 4d (four times original). New area = A/2 (halved).
- Substitute into Fourier’s law for the new configuration.

3. Calculations with intermediate steps
- Q̇_new = k (A/2) ΔT / (4d)
- Simplify numerator and denominator: Q̇_new = (k A ΔT) / (2 * 4 d) = (k A ΔT) / (8 d)
- Compare with initial: Q̇_new = (1/8) * (k A ΔT / d) = (1/8) Q̇_initial

4. Why the correct answer is correct
- The combined effect of quadrupling thickness (factor 1/4 change in Q̇) and halving area (factor 1/2 change) multiplies to 1/8. Thus the rate of heat loss decreases by a factor of 8.

5. Why the other options are incorrect
- (a) Quadrupled: wrong sign and magnitude — increasing thickness reduces, not increases, heat loss.
- (c) Increase by a factor of 8: opposite effect; actual change is a reduction.
- (d) Doubled: incorrect magnitude and direction; heat loss does not increase.

6. Conclusion
- The rate of heat loss decreases by a factor of 8, which matches the provided correct answer (b).

类似问题

Radiation is the transfer of heat by electromagnetic waves.

Select one means of controlling the fuel temperature on turbine-powered aircraft.

Radiation is heat.

What method of energy transfer requires no medium to travel?

Heat is

8. The heating load of a space depends primarily on solar gain and internal equipment load rather than infiltration or envelope heat loss.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单