A density glass bottle contains 44.25g of a liquid at 0(c) and 42.02 at 50(c). Calculate the real cubic expansivity of the liquid (Linear expansivity of glass=1.0*10^-5 K-1)?
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The linear expansivity of a metal P is twice that of another metal Q. When these materials are heated through the same temperature change, their increase in length is the same. Calculate the ratio of the original length of P to that of Q.
To calculate the real cubic expansivity of the liquid, we will use the formula:
β = (V₂ - V₁) / V₁ * (1 / (T₂ - T₁))
Where:
- β is the real cubic expansivity of the liquid
- V₁ is the initial volume of the liquid at temperature T₁ (0°C)
- V₂ is the final volume of the liquid at temperature T₂ (50°C)
- T₁ is the initial temperature (0°C)
- T₂ is the final temperature (50°C)
First, we need to calculate the volumes of the liquid at the given temperatures. We can use the formula:
V = m / ρ
Where:
- V is the volume
- m is the mass of the liquid
- ρ is the density of the liquid
At 0°C:
V₁ = 44.25g / ρ
At 50°C:
V₂ = 42.02g / ρ
Next, we need to calculate the difference in volumes, V₂ - V₁, and the temperature difference, T₂ - T₁.
Finally, we can substitute these values into the formula for β:
β = (V₂ - V₁) / V₁ * (1 / (T₂ - T₁))
Using the given values, we can calculate β.