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Calculate the temperature change of a 1 cm³ object if its volume expands by 0.0018 cm³ given a linear expansivity of 2.0 x 10⁻⁵ K⁻¹.
Physics
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Step-by-step solution
3 stepsTo find the temperature change , we use the formula for volume expansion:
where:
- is the change in volume
- is the coefficient of volume expansivity
- is the initial volume
- is the change in temperature
We are given:
- Initial volume () =
- Change in volume () =
- Linear expansivity () =
Calculate the coefficient of volume expansivity ().
For an isotropic material, the volume expansivity is approximately three times the linear expansivity:
Rearrange the volume expansion formula to solve for .
Substitute the values into the formula.
Since a change in temperature of is equivalent to a change of , the temperature change is .
Comparing this to the given options:
(A)
(B)
(C)
(D)The calculated value matches option (C).
The final answer is
\boxed{\text{(C) 30^\circ C}}
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