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有一刻度均匀，读数不准的温度计，在冰水混合物中示数为-2℃，在1标准大气压下的沸水中的示数为88℃，用此温度计测得一杯热水的温度是25℃，则热水的实际温度___...
Mar 19, 2024
有一刻度均匀，读数不准的温度计，在冰水混合物中示数为-2℃，在1标准大气压下的沸水中的示数为88℃，用此温度计测得一杯热水的温度是25℃，则热水的实际温度__________℃。
Solution
a
Identify the linear relationship between the thermometer's reading (R) and the actual temperature (T)
b
Establish two points to determine the line equation: Point 1 (R1, T1) = (-2, 0) and Point 2 (R2, T2) = (88, 100)
c
Calculate the slope (m) of the line: m=T2−T1R2−R1=100−088−(−2)=10090m = \frac{T2 - T1}{R2 - R1} = \frac{100 - 0}{88 - (-2)} = \frac{100}{90}
d
Calculate the y-intercept (b) of the line: T=mR+b⇒0=m(−2)+b⇒b=10090⋅2T = mR + b \Rightarrow 0 = m(-2) + b \Rightarrow b = \frac{100}{90} \cdot 2
e
Use the line equation to find the actual temperature (T) when the reading is 25℃: T=mR+bT = mR + b
f
Substitute R = 25 into the equation to find T: T=10090⋅25+20090T = \frac{100}{90} \cdot 25 + \frac{200}{90}
g
Simplify to get the actual temperature: T=2500+20090=270090=30T = \frac{2500 + 200}{90} = \frac{2700}{90} = 30
Answer
30℃
Key Concept
Linear interpolation: When two known points are used to find a linear equation that relates two variables, in this case, the thermometer's reading and the actual temperature.
Explanation
The actual temperature of the hot water is calculated by using the linear relationship between the inaccurate thermometer's readings and the known fixed points of water's freezing and boiling temperatures under standard atmospheric pressure.
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