Main Answer:
The change in the density of saturated liquid R-134a when cooled from 10°C to 0°C at constant pressure can be determined using the coefficient of volume expansion. The new density is approximately 1268 kg/m³.
Step-by-step explanation:
The coefficient of volume expansion (? = 0.00269 K⁻¹) provides a measure of how the volume of a substance changes with temperature. To find the change in density, we use the formula ΔV = V₀ * β * ΔT, where ΔV is the change in volume, V₀ is the initial volume, β is the coefficient of volume expansion, and ΔT is the change in temperature.
In this case, we calculate the change in temperature (ΔT) as (0°C - 10°C) = -10°C. The average temperature is (10°C + 0°C) / 2 = 5°C. Using the initial density (?1 = 1261 kg/m³) and rearranging the formula for density (ρ = m/V), where m is mass and V is volume, we find the initial volume V₀.
Then, applying the formula for ΔV, we find the change in volume. Finally, using the rearranged density formula with the new volume, we determine the new density at 0°C. The result is an approximate density of 1268 kg/m³.
This change in density is crucial in understanding the behavior of the refrigerant under different temperature conditions. It allows engineers and scientists to optimize refrigeration systems and ensure efficient heat transfer.