The coefficient of linear expansion for a silver

strip is 1.9 × 10−5
/
◦C.
What is its length on a hot day when the
temperature is 32◦C if the strip is 1.4 m long
when it is −15◦C?
Answer in units of m Your answer must be
within ± 1.0%

L = Lo + a*(T-To)Lo

L = 1.4 + 1.95*10^-5(32-(-15))1.4 =
1.401283 m.

To find the length of the silver strip on a hot day when the temperature is 32°C, we need to calculate the linear expansion. The linear expansion is given by the formula:

ΔL = α * L0 * ΔT

Where:
ΔL is the change in length
α is the coefficient of linear expansion
L0 is the initial length
ΔT is the change in temperature

Given:
α = 1.9 × 10^-5 / °C (coefficient of linear expansion)
L0 = 1.4 m (initial length)
ΔT = 32°C - (-15°C) = 47°C (change in temperature)

Now, substitute the given values into the formula:

ΔL = (1.9 × 10^-5 / °C) * (1.4 m) * (47°C)

ΔL = 1.9 × 10^-5 * 1.4 * 47 * m

ΔL ≈ 0.119036 m

Finally, to find the length on the hot day, add the change in length to the initial length:

Length on hot day = L0 + ΔL

Length on hot day = 1.4 m + 0.119036 m

Length on hot day ≈ 1.519036 m

Therefore, the length of the silver strip on a hot day when the temperature is 32°C is approximately 1.519036 meters.

To check if the answer is within ±1.0%:
Percentage change = (ΔL / L0) * 100

Percentage change = (0.119036 m / 1.4 m) * 100 ≈ 8.5025714%

Since the percentage change is approximately 8.50%, which is within ±1.0%, the answer is within the acceptable range.