A student measures the length of a brass rod with a steel tape at 20.0°C. The reading is 95.00 cm. What will the tape indicate for the length of the rod when the rod and the tape are at each of the following temperatures?
a)-20°C
b)60°C
I will be happy to critique your work on this.
new reading= L+deltaL
DeltaL=L*coeffthermalexpansion*deltaTemp
question: do you multiply the coefficient for steel in the equation and the coefficient for brass in a separate equation and add them together to get the answer?
To find the length of the brass rod when the temperature changes, we can use the linear expansion equation:
ΔL = α * L * ΔT
Where:
ΔL = change in length
α = coefficient of linear expansion
L = initial length
ΔT = change in temperature
The first step is to find the coefficient of linear expansion for brass. The coefficient of linear expansion for brass is approximately 19 × 10^(-6) / °C.
a) When the temperature is -20°C:
ΔT = -20 - 20 = -40°C (change in temperature)
L = 95 cm (initial length)
α = 19 × 10^(-6) / °C (coefficient of linear expansion)
ΔL = α * L * ΔT
ΔL = 19 × 10^(-6) / °C * 95 cm * -40°C
ΔL = -72.2 × 10^(-3) cm
The change in length is -72.2 × 10^(-3) cm, which means the tape will indicate a shorter length.
New length = initial length + change in length
New length = 95 cm + -72.2 × 10^(-3) cm
New length = 94.9278 cm
Therefore, the tape will indicate a length of approximately 94.9278 cm when the temperature is -20°C.
b) When the temperature is 60°C:
ΔT = 60 - 20 = 40°C (change in temperature)
L = 95 cm (initial length)
α = 19 × 10^(-6) / °C (coefficient of linear expansion)
ΔL = α * L * ΔT
ΔL = 19 × 10^(-6) / °C * 95 cm * 40°C
ΔL = 72.2 × 10^(-3) cm
The change in length is 72.2 × 10^(-3) cm, which means the tape will indicate a longer length.
New length = initial length + change in length
New length = 95 cm + 72.2 × 10^(-3) cm
New length = 95.0722 cm
Therefore, the tape will indicate a length of approximately 95.0722 cm when the temperature is 60°C.
To solve this problem, we need to take into account the thermal expansion of both the brass rod and the steel tape. The length of an object typically increases with an increase in temperature, and decreases with a decrease in temperature. The amount of expansion depends on the material's coefficient of linear expansion.
Let's find the coefficient of linear expansion for both brass and steel:
1. Brass: The coefficient of linear expansion for brass is typically around 19 x 10^(-6) per degree Celsius (19 x 10^(-6)/°C).
2. Steel: The coefficient of linear expansion for steel is about 12 x 10^(-6) per degree Celsius (12 x 10^(-6)/°C).
Using these coefficients, we can calculate the length of the rod at the given temperatures:
a) -20°C:
We need to calculate the new length of the rod when it is at -20°C.
The formula for thermal expansion is: ΔL = L * α * ΔT, where ΔL is the change in length, L is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature.
Let's calculate the change in length for the rod:
ΔL = (95.00 cm) * (19 x 10^(-6)/°C) * (-20°C - 20.0°C)
ΔL = (95.00 cm) * (19 x 10^(-6)/°C) * (-40°C)
The negative sign in front of ΔT accounts for the decrease in temperature. Solving this equation will give us the change in length.
b) 60°C:
We need to calculate the new length of the rod when it is at 60°C.
Using the same formula, we can calculate the change in length for the rod:
ΔL = (95.00 cm) * (19 x 10^(-6)/°C) * (60°C - 20.0°C)
ΔL = (95.00 cm) * (19 x 10^(-6)/°C) * (40°C)
Now, we can find the final length of the rod at each temperature:
a) -20°C:
Length at -20°C = 95.00 cm + ΔL
b) 60°C:
Length at 60°C = 95.00 cm + ΔL
By substituting the calculated ΔL values into these equations, we can find the final length of the rod at each given temperature.