Thermodynamics

Classical Mechanics Level 2

Which temperature has 1 0 ∘ C 10^\circ\text{C} difference in Celsius and Fahrenheit scale?

22. 5 ∘ C 22.5^\circ C or 23. 5 ∘ F 23.5^\circ F and 16. 5 ∘ C 16.5 ^\circ C or 67. 5 ∘ F 67.5^\circ F − 22. 5 ∘ C -22.5 ^\circ C or − 56. 5 ∘ F -56.5^\circ F and − 47. 5 ∘ C -47.5^\circ C or − 27. 5 ∘ F -27.5^\circ F − 52. 5 ∘ C -52.5 ^\circ C or − 62. 5 ∘ F -62.5 ^\circ F and − 27. 5 ∘ C -27.5 ^\circ C or − 17. 5 ∘ F -17.5^\circ F 42. 5 ∘ C 42.5^\circ C or 26. 5 ∘ F 26.5^\circ F and 13. 5 ∘ C 13.5 ^\circ C or 58. 5 ∘ F 58.5^\circ F

Nazmus Sakib by Nazmus sakib , 24, Bangladesh

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1 solution

Nazmus Sakib
Sep 10, 2017

Suppose,

  • The value in Fahrenheit scale = x = x

  • The value in Celsius scale = x ± 10 =x \pm 10

We know that, F − 32 9 = C 5 \dfrac{F-32}{9} =\dfrac{C}{5}

Now, for F = x F=x and C = x + 10 C=x+10 we will get

x − 32 9 = x + 10 5 \dfrac{x-32}{9}= \dfrac{x+10}{5}

⟹ 9 x + 90 = 5 x − 160 \implies 9x+90=5x-160

⟹ x = − 62.5 \implies x= -62.5 ∘ F ^ \circ F

So C = − 62.5 + 10 = − 52.5 C= -62.5+10 =-52.5 ∘ C ^ \circ C

Again, for F = x F=x and C = ( x − 10 ) C=(x-10) we will get,

x − 32 9 = x − 10 5 \dfrac{x-32}{9} = \dfrac{x-10}{5}

⟹ x = − 17.5 \implies x = -17.5 ∘ F ^ \circ F

Hence C = − 17.5 − 10 = − 27.5 C= -17.5-10 = -27.5 ∘ F ^ \circ F

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