Question

Різниця довжин залізної та мідної лінійок повинна дорівнювати 10 см при будь-якій температурі. Якими мають бути довжини цих лінійок при 0⁰C? Допоможіть, будь ласка! ​

Answer 1

Difference in Length of Iron and Copper Rulers at Different Temperatures

To determine the difference in length between an iron ruler and a copper ruler at different temperatures, we need to consider the coefficient of linear expansion for each material. The coefficient of linear expansion is a measure of how much a material expands or contracts when its temperature changes.

The coefficient of linear expansion for iron is approximately 0.000012 per degree Celsius. This means that for every degree Celsius increase in temperature, the length of an iron ruler will increase by 0.000012 times its original length.

The coefficient of linear expansion for copper is approximately 0.000016 per degree Celsius. This means that for every degree Celsius increase in temperature, the length of a copper ruler will increase by 0.000016 times its original length.

Calculating the Lengths at 0°C

To calculate the lengths of the iron and copper rulers at 0°C, we can use the formula:

Final Length = Initial Length + (Coefficient of Linear Expansion * Change in Temperature * Initial Length)

Since we want the difference in length between the two rulers to be 10 cm at any temperature, we can set up the following equation:

Length of Iron Ruler at 0°C - Length of Copper Ruler at 0°C = 10 cm

Let's solve this equation to find the lengths of the iron and copper rulers at 0°C.

Let's assume the initial lengths of both rulers are the same, denoted by L.

For the iron ruler at 0°C: L + (0.000012 * 0 * L) = L

For the copper ruler at 0°C: L + (0.000016 * 0 * L) = L

As we can see, the lengths of both rulers at 0°C will be equal to their initial lengths, which is L.

Therefore, the lengths of the iron and copper rulers at 0°C should be the same as their initial lengths.

Please note that the calculations above assume a linear relationship between temperature and length, and they are based on the coefficients of linear expansion provided. The actual behavior of materials may vary slightly due to other factors.