The diameter of a brass ring at 30 °C is 50.0 cm. To what temperature must this ring be heated to increase its diameter to 50.29 cm? [ linear expansivity of brass = 1.9 x 10\(^{-5}\) K\(^{-1}\)]
152.6 °C
182.6 °C
306.1 °C
335.3 °C
Explanation
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The chosen answer (option A) is wrong. The correct answer is option D.
To start with, you are not supposed to convert since the options are in Celsius. However even if you choose to convert you will still get your answer as option D not A.
Linear expansivity = L2−L1/L1(T2−T1)
1.9 x 10^−5= 0.29/50∗(T2−303)
1.9 x 10^−5* 50 (T2 - 303) = 0.29
50(T2 -303) =0.29/1.9*10^-5
Expanding, we have
50T2 - 15150 = 15,263.158
50T2 = 15,263.158 +15,150
50T2 = 30,413.158
T2 = 608.263 kelvin
T2 = 608.263 - 273
T2 = 335.236°C
Option D
i dont think this answer is correct though
why convert it the Kelvin when the options are clearly in degree Celcius
The chosen answer (option A) is wrong. The correct answer is option D.
To start with, you are not supposed to convert since the options are in Celsius. However even if you choose to convert you will still get your answer as option D not A.
Linear expansivity = L2−L1/L1(T2−T1)
1.9 x 10^−5= 0.29/50∗(T2−303)
1.9 x 10^−5* 50 (T2 - 303) = 0.29
50(T2 -303) =0.29/1.9*10^-5
Expanding, we have
50T2 - 15150 = 15,263.158
50T2 = 15,263.158 +15,150
50T2 = 30,413.158
T2 = 608.263 kelvin
T2 = 608.263 - 273
T2 = 335.236°C
Option D
T2 = 0.2950∗1.9∗10−5
+ 303
T2 = 152.6 °C
Greetings, The Myschool Team.
The correct answer is D(335.3°C) and not C(301.6°C). You provided a fine explanation of this. However, you forgot to add 30 to the answer gotten by simplifying the fraction. It is the fractional part that gives 306.1°C; adding 30°C to this then gives us the correct answer, which is described by option D(335.3°C). Thus, the correct answer is D(335.3 °C) and not C (306.1 °C). Please the necessary corrections should be made. Thank you.
Please there is a mistake in your calculations around the ending part of it after summing up everything you would get 335.5°C check again
