Answer:
The new temperature is [tex]T_1 = 60.78^oC[/tex]
Explanation:
From the question we are told that
The coefficient of linear expansion is [tex]\sigma = 122 *10^{-6} \ ^oC^{-1}[/tex]
The temperature is [tex]T = 20.0 ^oC[/tex]
The radius of the frames is [tex]r = 2.00 \ cm = 0.02 \ m[/tex]
The new radius is [tex]r_2 = 2.01 \ cm = 0.021 \ m[/tex]
The change in radius is mathematically represented as
[tex]\Delta r = r_1 -r[/tex]
substituting values
[tex]\Delta r = 2.01 - 2.00[/tex]
[tex]\Delta r = 0.01 \ m[/tex]
The increase in radius can also be mathematically represented as
[tex]\Delta r = r * \sigma (T_1 -T)[/tex]
Where [tex]T_1[/tex] is the the new temperature , making it the subject we have
[tex]T_1 = \frac{\Delta r}{r * \sigma } + T[/tex]
substituting value
[tex]T_1 = \frac{0.01}{2.01 *122*10^{-6} } + 20[/tex]
[tex]T_1 = 60.78^oC[/tex]
