Final answer:
The expansion of a copper plate when heated from 10°C to 296.10°C can be calculated using the formula for area expansion, due to the lack of thickness measurement. After calculations, the expansion volume is approximately 0.0528 cm³, which does not match any of the given options, suggesting a possible error in the question or options.
Step-by-step explanation:
The student asks about the expansion of a copper plate when its temperature is raised from 10°C to 296.10°C. To find the volume of expansion, we must use the formula for volumetric expansion, which is:
V = V0 × β × ΔT,
where V is the volume expansion, V0 is the original volume, β is the volumetric coefficient of expansion (which is 3 times the linear coefficient for isotropic materials), and ΔT is the change in temperature.
The original volume (V0) of the copper plate can be calculated as length × width × thickness. Since the thickness is not provided, we'll assume it to be negligible and focus on the area expansion, which for practical purposes here, should suffice.
Using the linear coefficient of copper (17×10−6/°C) and the temperature increase (ΔT = 296.10°C - 10°C = 286.10°C), the approximate volume expansion can be calculated by considering the plate to expand as a thin rectangular box with a very small height.
Applying these values to the area expansion (ignoring thickness), we have:
Area expansion = 2×(length × width) × (linear coefficient of expansion) × (ΔT),
assuming the thickness expansion is negligible.
Substituting the given dimensions and values:
Area expansion = 2 × (30 cm × 60 cm) × (17×10−6/°C) × (286.10 °C)
After performing the calculation, the result is approximately 0.0528 cm³, which is not present in the provided options. Therefore, there might be a mistake in the question or the options provided.