Density, Pressure in Liquids and Change of State
Density is a measure of how much mass is contained in a given volume of a substance, given by density = mass / volume, and is used to compare how tightly packed the particles of different materials or states of matter are. Pressure in a liquid, given by pressure = height x density x gravitational field strength (P = h x rho x g), increases with depth because the weight of the liquid above pushes down, and acts equally in all directions at a given depth. Change of state (melting, freezing, boiling, condensing, and sublimation) occurs at a constant temperature for a pure substance, because the energy transferred is used to break or form bonds between particles rather than to increase their kinetic energy; the specific latent heat needed for a change of state is calculated using energy = mass x specific latent heat.
Before you start
Make sure you're comfortable with these topics first:
Method
- For density questions, use density = mass / volume, rearranging as needed, and keep mass in kg (or g) and volume in m^3 (or cm^3), being consistent with the units the question uses.
- For a liquid pressure question, use pressure = height x density x gravitational field strength (P = h x rho x g), where height is the depth below the surface of the liquid, keeping height in metres, density in kg/m^3 and g in N/kg.
- Explain that liquid pressure increases with depth because there is more liquid, and therefore more weight, pushing down from above at greater depths, and that liquid pressure does not depend on the shape or width of the container.
- For change-of-state questions, identify which change is happening (melting, freezing, boiling, condensing or sublimation) and recall that temperature stays constant during the change, even though energy is still being transferred.
- Use energy = mass x specific latent heat (E = m x L), using the specific latent heat of fusion for melting or freezing, and the specific latent heat of vaporisation for boiling or condensing, substituting mass in kg and specific latent heat in J/kg.
- If a question also involves a temperature change before or after the change of state, calculate that part separately using energy = mass x specific heat capacity x temperature change, then add the two energy values together for the total.
Worked example
Calculate the pressure due to the water at a depth of 25 m below the surface of a lake. The density of water is 1000 kg/m^3 and g = 10 N/kg.
- Write down the equation for liquid pressure: pressure = height x density x gravitational field strength.
- Substitute the values: pressure = 25 x 1000 x 10.
- Calculate 25 x 1000 = 25000.
- Calculate 25000 x 10 = 250000.
- State the final answer with its unit: pressure = 250000 Pa (2.5 x 10^5 Pa).
Practice questions
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Q1State the equation for density.Show answer
Answer: Density = mass / volume.
Q2A block has a mass of 0.60 kg and a volume of 0.00020 m^3. Calculate its density.Show answer
Answer: 3000 kg/m^3 (0.60/0.00020).
Q3State why the pressure in a liquid increases with depth.Show answer
Answer: Because there is a greater weight of liquid above pushing down at greater depths.
Q4State why temperature stays constant while a substance is melting, even though energy is still being transferred to it.Show answer
Answer: The energy is used to break the bonds between particles (weaken the forces holding the solid structure together) rather than to increase their kinetic energy, so temperature does not rise.
Q5Calculate the pressure due to a liquid of density 800 kg/m^3 at a depth of 3.0 m. Use g = 10 N/kg.Show answer
Answer: 24000 Pa (3.0 x 800 x 10).
Q6The specific latent heat of fusion of ice is 334000 J/kg. Calculate the energy needed to melt 0.50 kg of ice at 0 degrees C. Use energy = mass x specific latent heat.Show answer
Answer: 167000 J (0.50 x 334000).
Q7State the name of the change of state where a solid turns directly into a gas without becoming a liquid.Show answer
Answer: Sublimation.
Exam-style questions
Written in the style of a IGCSE Science exam paper, with a full mark scheme.
The specific latent heat of vaporisation of water is 2260000 J/kg. Calculate the energy needed to boil away 0.020 kg of water that is already at 100 degrees C. Use energy = mass x specific latent heat.
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A 0.40 kg block of ice starts at -10 degrees C. Calculate the total energy needed to warm the ice to 0 degrees C and then completely melt it at 0 degrees C. The specific heat capacity of ice is 2100 J/(kg degrees C) and the specific latent heat of fusion of ice is 334000 J/kg. Show your working for each stage clearly.
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Free printable worksheet
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This topic is chapter 30 of IGCSE Science Workbook, the whole course as one free printable PDF.
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