Two students were investigating the effects of inserting a hot iron block into cool water. A [math: 4.20×102g] block of iron at 82.1 °C is placed in [math: 6.00×102g] of water at 32.2 °C. The specific heat capacities of iron and water respectively are [math: 4.50×102Jkg−1K−1] and [math: 4.20×103Jkg−1K−1]. It is observed that the iron block and the water both lose 2 degrees before being placed together. Calculate the final temperature (in °C) of the iron block.

Question

BlackTom AI · Accepted Answer

Heat lost by the iron equals heat gained by the water (isolated system). Use Q = m c ΔT with initial temperatures reduced by 2 °C as stated: iron Ti,Fe = 82.1 − 2 = 80.1 °C; water Ti,w = 32.2 − 2 = 30.2 °C.

1) Relevant knowledge
- Conservation of energy for thermal exchange: mFe cFe (Ti,Fe − Tf) = mW cW (Tf − Ti,w).
- Convert masses to kg and use given specific heats in J kg−1 K−1.

2) Values and conversions
- mFe = 4.20 × 10^2 g = 0.420 kg
- mW  = 6.00 × 10^2 g = 0.600 kg
- cFe = 4.50 × 10^2 J kg−1 K−1 = 450 J kg−1 K−1
- cW  = 4.20 × 10^3 J kg−1 K−1 = 4200 J kg−1 K−1
- Ti,Fe = 80.1 °C; Ti,w = 30.2 °C

3) Set up equation and show intermediate steps
- Left coefficient: mFe · cFe = 0.420 · 450 = 189 J K−1
- Right coefficient: mW · cW = 0.600 · 4200 = 2520 J K−1

Equation: 189(80.1 − Tf) = 2520(Tf − 30.2)

Expand:
189·80.1 − 189 Tf = 2520 Tf − 2520·30.2
15138.9 − 189 Tf = 2520 Tf − 76104

Collect Tf terms and constants:
15138.9 + 76104 = 2520 Tf + 189 Tf
91242.9 = 2709 Tf

Solve for Tf:
Tf = 91242.9 / 2709 ≈ 33.68095 °C

4) Why this answer is correct
The calculation directly enforces energy conservation with the correct, reduced initial temperatures. The large heat capacity of water (and its slightly larger mass) means the equilibrium temperature is pulled much closer to the water’s initial temperature (30.2 °C) than to the iron’s (80.1 °C); the computed value 33.68 °C reflects that.

5) Why other options are incorrect
- a. 35.68 °C corresponds to the same heat-balance calculation but using the original temperatures (82.1 and 32.2) without subtracting the 2 °C loss — it ignores the stated pre-cooling.
- c. 24.23 °C and d. 28.15 °C are too low; they would require the water to cool rather than warm or imply incorrect heat flow/magnitudes.

6) Conclusion
The correct final temperature of the iron block is 33.68 °C, matching answer b.

类似问题

Water has a high specific heat capacity; it takes a lot of energy--either gained or lost--to change its temperature. In the physical world, what does this mean?

The thermal behaviour of a material is characterised by the value of its

The thermal behaviour of a material is characterised by the value of its

____________ is the amount of heat required to raise the temperature of 1 gram of a substance 1 degree Celsius.

What is the formula of the energy required to change the temperature?

It is a well-known fact that water has a higher specific heat capacity than iron. Now, consider equal masses of water and iron that are initially in thermal equilibrium. The same amount of heat flow, 300 J, is added to each. Which statement is true?

Temperature of land rises more quickly than that of sea because

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