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°.
1-19.93 cm
2-19.69 cm
3-19.50 cm
4-19.09 cm
L = Lo + a(T-To)Lo = 20 cm
Lo + 19*10^-6(200-20)Lo = 20
Lo + 0.00342Lo = 20
1.00342Lo = 20
Lo = 19.93 cm. = Initial length.
To determine how long a piece of brass can be put in the available space and still fit at a higher temperature, 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
L is the original length
ΔT is the change in temperature
In this case, we want to find the maximum length at 200°C while starting with a length of 20.00 cm at 20°C.
ΔL = α * L * ΔT
ΔL = 19 × 10^-6/°C * 20.00 cm * (200 - 20) °C
ΔL = 19 × 10^-6/°C * 20.00 cm * 180 °C
ΔL = 0.0342 cm
To find the maximum length at 200°C, we can subtract the change in length from the original length:
Max length = L - ΔL
Max length = 20.00 cm - 0.0342 cm
Max length = 19.9658 cm
Rounding to two decimal places, the maximum length of the brass at 200°C while still fitting in the available space is 19.96 cm.
Therefore, the closest answer choice is option 1-19.93 cm.
To determine how long a piece of brass at 20°C can be put in the available 20.00 cm space and still fit at 200°C, we need to calculate the change in length of the brass due to the difference in temperature.
The linear expansion coefficient of brass is given as 19 × 10^-6/C°. This means that for every degree Celsius increase in temperature, the length of brass will increase by 19 × 10^-6 times its original length.
To calculate the change in length, we use the formula:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length
α is the linear expansion coefficient
L0 is the original length
ΔT is the change in temperature
In this case, the original length (L0) is the available space of 20.00 cm and the change in temperature (ΔT) is 200°C - 20°C = 180°C.
ΔL = (19 × 10^-6/C°) * (20.00 cm) * (180°C)
Calculating this expression gives us:
ΔL = 0.000342 cm
To find the new length of the brass, we subtract the change in length from the original length:
New length = L0 - ΔL
New length = 20.00 cm - 0.000342 cm
New length = 19.999658 cm
Rounded to the nearest hundredth of a centimeter, the new length of the brass at 200°C is approximately 19.99 cm.
None of the provided answer choices match exactly, but the closest option is:
3-19.50 cm
However, please note that this answer is an estimation and the exact length may differ slightly depending on the precision of the calculations and the accuracy of the linear expansion coefficient.