The density of measly is [tex]$1.36 \times 10^4 kgm ^{-3}$[/tex] at [tex]$O^{\circ} C$[/tex]. Calculate its value at [tex]$100^{\circ} C$[/tex] and [tex]$22^{\circ} C$[/tex]. Take cubic expansivity of meany as equal to [tex]$180 \times 10^{-6} K$[/tex]
Answer (2)
The density of measly at 10 0 ∘ C is approximately 13359.53 kg/m 3 , while at 2 2 ∘ C , it is about 13546.36 kg/m 3 . These values are derived using the formula for density change due to temperature variations. The calculations involve using the cubic expansivity of measly to account for the temperature differences.
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The density at a given temperature is calculated using the formula: ρ T = 1 + γ Δ T ρ 0 .
Calculate the density at 10 0 ∘ C : ρ 100 = 1 + ( 180 × 1 0 − 6 ) × 100 1.36 × 1 0 4 ≈ 13359.53 k g / m 3 .
Calculate the density at 2 2 ∘ C : ρ 22 = 1 + ( 180 × 1 0 − 6 ) × 22 1.36 × 1 0 4 ≈ 13546.36 k g / m 3 .
The density at 10 0 ∘ C is approximately 13359.53 k g / m 3 , and the density at 2 2 ∘ C is approximately 13546.36 k g / m 3 .
Explanation
Understanding the Problem We are given the density of measly at 0 ∘ C and the cubic expansivity. We need to find the density at 10 0 ∘ C and 2 2 ∘ C . The density at a different temperature can be calculated using the formula: ρ T = 1 + γ Δ T ρ 0 where ρ 0 is the initial density, γ is the cubic expansivity, and Δ T is the change in temperature.
Calculating Density at 100°C First, let's calculate the density at 10 0 ∘ C . The change in temperature is Δ T = 100 − 0 = 10 0 ∘ C . We have ρ 0 = 1.36 × 1 0 4 k g / m 3 and γ = 180 × 1 0 − 6 K − 1 . Plugging these values into the formula, we get: ρ 100 = 1 + ( 180 × 1 0 − 6 ) × 100 1.36 × 1 0 4 ρ 100 = 1 + 0.018 1.36 × 1 0 4 ρ 100 = 1.018 1.36 × 1 0 4 ρ 100 ≈ 13359.53 k g / m 3
Calculating Density at 22°C Next, let's calculate the density at 2 2 ∘ C . The change in temperature is Δ T = 22 − 0 = 2 2 ∘ C . Using the same formula, we get: ρ 22 = 1 + ( 180 × 1 0 − 6 ) × 22 1.36 × 1 0 4 ρ 22 = 1 + 0.00396 1.36 × 1 0 4 ρ 22 = 1.00396 1.36 × 1 0 4 ρ 22 ≈ 13546.36 k g / m 3
Final Answer Therefore, the density of measly at 10 0 ∘ C is approximately 13359.53 k g / m 3 , and the density at 2 2 ∘ C is approximately 13546.36 k g / m 3 .
Examples
Understanding how density changes with temperature is crucial in many real-world applications. For example, in civil engineering, the expansion and contraction of materials like concrete and steel due to temperature variations must be considered to ensure the structural integrity of buildings and bridges. Similarly, in the food industry, density changes affect the processing and packaging of various products, ensuring consistent quality and volume. In meteorology, understanding the density of air at different temperatures helps predict weather patterns and atmospheric conditions. These principles ensure safety, efficiency, and precision across diverse fields.
