A copper telephone wire has essentially no
sag between poles 30 m apart on a winter day
when the temperature is −16◦C.
How much longer is the wire on a summer
day when the temperature is 26 ◦C? Assume
that the thermal coefficient of copper
is constant throughout this range at its room
temperature value of 1.7 × 10−5 (◦C)−1.
Answer in units of cm.
Increase = (26-(-16))C*1.7*10^-5/C*30cm
= 42*1.7*10^-5 * 30cm =0.02142 cm.
Well, let me put on my comedy hat and try to answer your question with a touch of humor.
Ahem, let's see. So you're asking about the sag in a copper telephone wire... quite the flexible topic! Now, I must say, this sag is like the difference between your winter and summer moods – a little temperature variation can really change things!
Now, in order to calculate the length difference, we can use a formula that relates the temperature change to the change in length. The formula is ΔL = α * L * ΔT, where ΔL is the change in length, α is the thermal coefficient, L is the original length, and ΔT is the change in temperature.
Given that α for copper is 1.7 × 10^(-5) (°C)^(-1), we can now calculate the change in length.
So, substituting the values, we have ΔL = (1.7 × 10^(-5)) * 30 m * (26°C - (-16°C)). But, we need to remember to convert meters to centimeters for the answer.
So, drumroll please... the longer length of the wire on a summer day when compared to winter would be approximately ΔL centimeters.
I hope that brings a little warmth and laughter to your question!
To solve this problem, we can use the formula for thermal expansion:
ΔL = αLΔT
Where:
ΔL is the change in length of the wire
α is the thermal coefficient of copper (1.7 × 10^-5 (◦C)^-1)
L is the original length of the wire (30 m)
ΔT is the change in temperature (26 ◦C - (-16 ◦C) = 42 ◦C)
Now let's calculate the change in length of the wire on a summer day:
ΔL = (1.7 × 10^-5 (◦C)^-1) * (30 m) * (42 ◦C)
ΔL = 2.7142 × 10^-2 m
To convert this to centimeters, we multiply by 100:
ΔL = 2.7142 × 10^-2 m * 100 cm/m
ΔL ≈ 2.7142 cm
Therefore, the wire is approximately 2.7142 cm longer on a summer day when the temperature is 26 ◦C.
To find out how much longer the wire is on a summer day compared to a winter day, we need to calculate the change in length of the wire due to temperature variation.
The formula to calculate the change in length of a material due to temperature variation is:
ΔL = L * α * ΔT
Where:
ΔL is the change in length,
L is the original length of the wire,
α is the thermal coefficient of copper, and
ΔT is the change in temperature.
Given Information:
L = 30 m (length between poles)
ΔT = (26 - (-16)) = 42 ◦C (change in temperature)
α = 1.7 × 10^(-5) (◦C)^-1 (thermal coefficient of copper)
Now, let's substitute the given values into the formula to calculate the change in length:
ΔL = (30 m) * (1.7 × 10^(-5) (◦C)^-1) * (42 ◦C)
Calculating the above expression:
ΔL = 30 * 1.7 × 10^(-5) * 42 = 0.021 m
Now, since the answer needs to be in centimeters, we can convert the result to cm:
1 m = 100 cm
0.021 m * 100 cm/m = 2.1 cm
Therefore, the copper telephone wire is 2.1 cm longer on a summer day when the temperature is 26 ◦C compared to a winter day when the temperature is −16◦C.