A steel rod with an original length of 2 meters undergoes a temperature increase. If the coefficient of linear thermal expansion of steel is 1.2×10−5 per degree Celsius, and the temperature change is 50 degrees Celsius, what will be the final length of the steel rod?
Question
A steel rod with an original length of 2 meters undergoes a temperature increase. If the coefficient of linear thermal expansion of steel is 1.2×10−5 per degree Celsius, and the temperature change is 50 degrees Celsius, what will be the final length of the steel rod?
Solution
The change in length (ΔL) due to thermal expansion can be calculated using the formula:
ΔL = α * L0 * ΔT
where: α is the coefficient of linear expansion, L0 is the original length, and ΔT is the change in temperature.
Given: α = 1.2×10−5 per degree Celsius, L0 = 2 meters, and ΔT = 50 degrees Celsius,
we can substitute these values into the formula:
ΔL = 1.2×10−5 * 2 * 50 = 0.0012 meters.
The final length of the rod is the original length plus the change in length:
L = L0 + ΔL = 2 + 0.0012 = 2.0012 meters.
So, the final length of the steel rod after a temperature increase of 50 degrees Celsius will be 2.0012 meters.
Similar Questions
Thermal Expansion: An aluminum rod is10.0cmlong and a steel rod is80.0cmlong when both rods are at a temperature of15\\\\deg C. Both rods have the same diameter. now joined end-to-end to form a rod90.0cmlong. If the temperature is now raised from15\\\\deg Cto90\\\\deg C, what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is2.4\\\\times 10^(-5)K^(-1)and that of steel is1.2\\\\times 10^(-5)K^(-1).\\n0.90mm\\n0.99mm\\n0.72mm\\n0.63mm\\n0.81mm
A man measures the length of a steel rod by a 1 m long steel tape on a sunny day when thetemperature is 47.0 °C. The length of steel rod is found to be 60.00 cm. If the steel tape is calibratedat room temperature, what is the actual length of the rod on that day?[Use Coefficient of linear expansion of steel = 1.20 × 10–5 K-1 ]
A steel beam 20 meters long is subjected to a temperature increase of 30°C. If the coefficient of linear expansion for steel is1.2x10⁻⁵/°C, how much does the beam lengthen?Select one:a.7.2mmb.7.2cmc.72mmd.72cm
A copper wire has an original length of 3 meters. If the wire undergoes a temperature increase, and its final length is measured to be 3.012 meters, what was the change in temperature? (The coefficient of linear thermal expansion for copper is 1.7×10−5 per degree Celsius).
A 2.00-kg copper rod is 40.00 cm long at 23°C. If 50,000 J are transferred to the rod by heat, what is its change in length? (ccopper = 387 J/kg·°C and αcopper = 17 × 10-6/°C)Select one:a.0.022 cmb.More information is needed.c.0.044 cmd.0.055 cm
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.