ICSE Class 8 Answered
A faulty centigrade thermometer is examined. The upper and lower points are found to be 99.5 and 0.5. which is the correct temperature if this faulty thermometer reads 15.5?
Asked by csr.goutham | 06 Feb, 2019, 09:34: PM
Expert Answer
It is assumed that lower and upper limits of faulty temperature 0.5 and 99.5 are corresponding
to the true temperatures 0°C and 100°C
Let FT be the faulty temperature and TT be true temperature.
Let us assume both the temperatures are related by, TT = a + b×FT .......................(1)
where a and b are constants to be determined.
we have FT = 0.5 when TT = 0°C , 0 = a+ b×0.5 ..........................(2)
we have FT = 99.5 when TT = 100°C , 100 = a+ b×99.5 ........................(3)
By subtracting (3) from (2), we have, 99×b = 100 or b = (100/99)
By substituting b in eqn.(2), we get a = - (100/99)×0.5 = - 50/99
Hence eqn.(1) can be written as, TT = -(50/99) + (100/99)×FT ......................(4)
if FT = 15.5, from eqn.(4) we get TT = -(50/99) +(100/99)×(15.5) ≈ 15.15 ºC
Answered by Thiyagarajan K | 06 Feb, 2019, 10:48: PM
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