A container holds 1 litre of water at 20°C. Find its volume at 80°C using a constant volume-expansion coefficient β = 2.1×10⁻⁴ °C⁻¹.

Solution & explanation

1. Given: V₀ = 1 litre, β = 2.1×10⁻⁴ °C⁻¹.

2. Convert litres to cubic centimetres.

   $$V_0=1000$$

3. Calculate the temperature interval.

   $${\Delta }_T=80-20=60$$

4. Write the volume-increase formula.

   $${\Delta }_V={\Delta }_T\times V_0\times \beta$$

5. Substitute without omitting the original volume.

   $${\Delta }_V=\frac{126000.0}{10000}$$

6. Calculate increase in cm³.

   $${\Delta }_V=12.6$$

7. Add increase to initial volume.

   $$V=12.6+1000=1012.6$$

8. State the result with units: 1012.6 cm³ = 1.0126 litres.

V = 1012.6 cm³