a steel rod was found to be 2 meters long at 20 degree celcious.when measured by a standard brass scale of length 1 meter at 0 degree celcious.find out the length of the same steel rod at 50 degree celcious as measured by the same brass scale at 40 degree celcious.where steel=5×10 to the power-four Kelvin inverse and brass=6×10 to the power-four celcious inverse
newlength=2m+(2*5e-4)(20)-2(6e-4)(40)=1.97m
check my work
To find out the length of the steel rod at 50 degrees Celsius, as measured by the same brass scale at 40 degrees Celsius, you need to consider the coefficient of linear expansion for both steel and brass, as well as the change in temperature.
The formula to calculate the change in length of an object due to temperature is given by:
ΔL = α * L0 * ΔT
where:
ΔL is the change in length
α is the coefficient of linear expansion
L0 is the initial length
ΔT is the change in temperature
For the steel rod:
Coefficient of linear expansion (α) = 5 × 10^(-4) K^(-1)
Initial length (L0) = 2 meters
Change in temperature (ΔT) = (50 - 20) = 30 degrees Celsius
Calculating the change in length of the steel rod:
ΔL_steel = α * L0 * ΔT
= (5 × 10^(-4) K^(-1)) * (2 meters) * (30 degrees Celsius)
Next, we need to convert the change in temperature from Celsius to Kelvin. The formula to convert from Celsius to Kelvin is:
T (in Kelvin) = T (in Celsius) + 273.15
For the brass scale:
Coefficient of linear expansion (α) = 6 × 10^(-4) °C^(-1)
Initial length (L0) = 1 meter
Change in temperature (ΔT) = (40 - 0) = 40 degrees Celsius
Calculating the change in length of the brass scale:
ΔL_brass = α * L0 * ΔT
= (6 × 10^(-4) °C^(-1)) * (1 meter) * (40 degrees Celsius)
Now, we can find the length of the steel rod at 50 degrees Celsius, as measured by the same brass scale at 40 degrees Celsius:
Length_steel_at_50C = Initial length + ΔL_steel - ΔL_brass
Substituting the calculated values:
Length_steel_at_50C = 2 meters + ΔL_steel - ΔL_brass
Finally, you need to plug in the calculated values for ΔL_steel and ΔL_brass to find the length of the steel rod at 50 degrees Celsius.