A glass bottle of initial volume 2 x 10\(^4\) cm\(^3\) is heated from 20ºC to 50ºC. If the linear expansivity of glass is 9 x 10\(^{-6}\)K\(^{-1}\), the volume of the bottle at 50ºC is
A
20016.2cm3
B
20005.4cm3
C
20008.1cm3
D
20013.5cm3
Verified Correct Answer: A.
Physical Principles & Numerical Solution
\(\gamma = \frac{V_2 - V_1}{V(\theta)}\)
\(3(9 \times 10^4) = \frac{V_2 - 2 \times 10^4}{2 \times 10^4(30)}\)
V\(_2\) - 2 x 10\(^4\) = 2 x 10\(^4\) (30) x 3 (9 x 10\(^{-6}\))
V\(_2\) = 2 x 10\(^4\) (30) x 3 (9 x 10\(^{-6}\)) + 2 x 10\(^4\)
V\(_2\) = 16.2 + 2 x 10\(^4\)
V\(_2\) = 20016.2cm3
Source: Myschool Past Questions Archive (Record #26995)