Question

The density of a fluid decreases by 3 percent at constant pressure when its temperature increases by 16°C. The coefficient of volume expansion of this fluid is K-1. Solve this problem using appropriate software. Multiple Choice a.0.0019 b.0.0025 c.0.025 d.0.19

Answer 1

The coefficient of volume expansion for a fluid whose density decreases by 3% with a 16°C increase in temperature is approximately 0.0019 K⁻¹.

Step-by-step explanation:

The student's question involves the concept of the coefficient of volume expansion, which in physics, indicates how the size of an object changes with a change in temperature at constant pressure. Given that the density of a fluid decreases by 3 percent when the temperature increases by 16°C, the coefficient of volume expansion (β) can be found using the formula β = ΔV/(V₀ΔT), where ΔV is the change in volume, V₀ is the initial volume, and ΔT is the change in temperature.

Since density ρ is inversely proportional to volume V (as ρ = mass/V), a decrease in density by 3% implies an increase in volume by 3%. Thus, if ΔT is 16°C, then the coefficient of volume expansion can be calculated as β = (0.03)/(16) = 0.001875 K⁻¹, which is approximately 0.0019 K⁻¹ when rounded to three significant figures.