20.00 cm of space is available. How long a piece of brass at 20°C can be put there and still fit at 200°C? Brass has a linear expansion coefficient of 19 × 10^-6/C°.
19.93 cm
19.69 cm
19.50 cm
19.09 cm
deltaL=L*coeff*delta temp
deltaL=L 19E-6 * 180
deltaL/L=19E-6 * 180
Now, L+deltaL=20.00 cm
deltaL/L +1=20.00/L
19E-6 * 180+1=20.00/L
L=20.00/(19E-6 * 180+1) and that answer is above.
To determine the length of the brass at 200°C, we can use the formula for linear expansion:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the linear expansion coefficient of brass (19 × 10^-6/C°)
L is the original length at 20°C
ΔT is the change in temperature (200°C - 20°C = 180°C)
We can rearrange the formula to solve for the change in length:
ΔL = α * L * ΔT
ΔL = (19 × 10^-6/C°) * 20.00 cm * 180°C
ΔL ≈ 0.0342 cm
To find the final length at 200°C, we subtract the change in length from the original length:
Length at 200°C = Length at 20°C - ΔL
Length at 200°C = 20.00 cm - 0.0342 cm
Length at 200°C ≈ 19.966 cm
Therefore, a piece of brass at 20°C can be put into the available 20.00 cm of space and still fit at 200°C, with a length of approximately 19.966 cm.
None of the provided answer options match exactly, but the closest option is 19.93 cm.