Final answer:
The diameter of the iron lid would increase by 0.438 mm after being heated from 20°C to 70°C, due to the higher coefficient of thermal expansion of iron compared to glass.
Step-by-step explanation:
When a metal lid is heated, its diameter will increase more than a glass jar's diameter would if they were both heated by the same amount. This is because metals typically have a higher coefficient of thermal expansion than glass does. To calculate the mismatch size after heating the lid from 20°C to 70°C, we need to know the coefficient of thermal expansion for the iron lid.
Let's assume that the average coefficient of thermal expansion for iron is approximately α = 12 x 10-6 / °C. Using the formula for linear expansion ΔL = α L₀ ΔT, where ΔL is the change in length, L₀ is the original length (730 mm for the lid), and ΔT is the change in temperature (70°C - 20°C = 50°C), we can calculate the new diameter of the lid after heating.
The change in diameter of the lid would be:
ΔD = α D₀ ΔT
ΔD = (12 x 10-6/ °C) x 730 mm x 50°C
ΔD = 0.438 mm (increased diameter)
Therefore, after heating, the diameter of the lid will be:
New diameter = Original diameter + ΔD
New diameter = 730 mm + 0.438 mm
New diameter = 730.438 mm
So, heating the iron lid under hot water will cause it to expand by 0.438 mm, increasing the size of the mismatch between the lid and the jar by the same amount, making it potentially easier to open the jar.