The density of gasoline at 0^∘ C is 0.68 ×10^3 kg / m^3 .(a) What is the density on a hot day, w

step 1 The density of gasoline at 0 .6 .6 .8 times 10 to the 3 kilograms per meter cube. What is the de

The density of gasoline at 0^∘ C is 0.68 ×10^3 kg / m^3 .(a)...

The density of gasoline at $0^{\circ} \mathrm{C}$ is $0.68 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .(a)$ What is the density on a hot day, when the temperature is $35^{\circ} \mathrm{C}$ ? (b) What is the percent change in density?

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Key Concepts

Thermal Expansion

Thermal expansion is the tendency of a material to change its dimensions—typically increasing its volume—when its temperature increases. In liquids, this effect is quantified by the coefficient of volumetric expansion, which relates the fractional change in volume to the change in temperature. This concept is crucial in understanding how a substance’s volume and, consequently, its density change when heated.

Density (Mass-Volume Relationship)

Density is defined as mass per unit volume. When the temperature of a substance increases and it undergoes thermal expansion, its volume increases while its mass remains constant, leading to a decrease in density. This inverse relationship is key to calculating the new density when a fluid is heated.

Percent Change Calculation

Percent change is a method of comparing the magnitude of a change relative to the original amount, expressed as a percentage. In the context of density changes, it involves determining the difference between the initial and final densities, dividing by the initial density, and multiplying by 100 to express the result as a percentage. This calculation helps quantify how significantly the density of a substance is altered due to temperature variations.

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