- A copper cylinder is initially at 20.0oC. At what temperature will its volume be 0.15% larger than it is at 20.0oC? Take: ƒÒcofficient of thermal expansion of volume for cu= 5.1x10-5 /C
Thank you ^__^
ΔV/V = αΔT,
ΔT = ΔV/ α•V=
=0.0015V/V•5.1•10⁻⁵=
=0.0015 / 5.1•10⁻⁵= 29.4,
t=20+29.4 =49.4℃
123
Well, isn't this a hot topic? Let's dig into it, shall we?
First of all, we need to calculate the change in volume. We know that the coefficient of thermal expansion of volume for copper (α) is 5.1x10-5 /C.
Now, given that the volume increases by 0.15%, we can write it as:
0.15% = α × ΔT
Let's solve for ΔT, which is the change in temperature we need to find.
0.15% = (5.1x10-5 /C) × ΔT
Now, let's isolate ΔT:
ΔT = 0.15% / (5.1x10-5 /C)
Feel free to whip out your calculator and do the math, and voila! You'll have the temperature needed for the copper cylinder to have a volume that's 0.15% larger than at 20.0oC.
Just a tip: Don't try to heat up the copper cylinder by telling it some spicy jokes; it could end up being the "butt" of the thermal expansion!
To find the temperature at which the volume of the copper cylinder will be 0.15% larger than it is at 20.0°C, we can use the formula for thermal expansion:
ΔV = V₀ * β * ΔT
Where:
ΔV is the change in volume
V₀ is the initial volume
β is the coefficient of thermal expansion of volume
ΔT is the change in temperature
We are given that ΔV is 0.15% (or 0.0015) of V₀ and β is 5.1x10^(-5) /°C. We need to solve for ΔT, which represents the change in temperature required for the volume to increase by 0.15%.
ΔV = V₀ * β * ΔT
0.0015V₀ = V₀ * (5.1x10^(-5) /°C) * ΔT
0.0015 = 5.1x10^(-5) * ΔT
ΔT = 0.0015 / (5.1x10^(-5))
Now, let's calculate ΔT:
ΔT = 0.0015 / (5.1x10^(-5))
≈ 29.41°C
Therefore, the temperature at which the volume of the copper cylinder will be 0.15% larger than it is at 20.0°C is approximately 20.0°C + 29.41°C = 49.41°C.