Question

Suppose a glass bottle with volume 0.027 m3 if filled to the brim with a fluid with unknown coefficient of volume expansion. When warmed by 6.8 oC, 18 mL spill onto the lab table. If the glass has linear coefficient 2.2 x 10-5 K-1, calculate the unknown volume coefficient of the fluid in (koC)-1. There are 1000 oC = 1 KoC.

Answer 1

To calculate the unknown volume coefficient of expansion of the fluid, use the equation AV / V₀ = B × ΔT. The unknown volume coefficient of expansion is approximately 0.059 (koC)-1.

Step-by-step explanation:

To calculate the unknown volume coefficient of expansion of the fluid, we can use the equation:

AV / V₀ = B × ΔT

where AV is the change in volume, V₀ is the initial volume, B is the coefficient of volume expansion, and ΔT is the change in temperature.

Substituting the given values, we have: 0.018 L / 0.027 m³ = B × 6.8 oC

Simplifying the equation, we find that the unknown volume coefficient of expansion is approximately 0.059 (koC)-1.

Answer 2

The unknown volume coefficient of the fluid is approximately 0.0735 (koC)-1.

Step-by-step explanation:

To calculate the unknown volume coefficient of the fluid, we can use the formula for volume expansion:

V₂ = V₁(1 + B∆T) Where V₂ is the final volume, V₁ is the initial volume, B is the volume coefficient of expansion, and ∆T is the temperature change. Given that 18 mL of fluid spills out when warmed by 6.8 °C, we can convert the volume to cubic meters by dividing by 1000. So V₁ = 18/1000 = 0.018 m³. Plugging in the known values, we have: 0.027 = 0.018(1 + B(6.8)) Simplifying the equation, we get: 1 + B(6.8) = 0.027/0.018, 1 + B(6.8) = 1.5, B(6.8) = 1.5 - 1, B(6.8) = 0.5

Now, we can divide both sides by 6.8 to find B: B = 0.5/6.8 B ≈ 0.0735 (koC)-1