(a) State two differences between boiling and evaporation.
(b) A closed inexpansibie vessel contains air saturated with water vapour at 77°C. The total pressure in the vessel is 1007 mmHg. Calculate the new pressure in the vessel if the temperature is reduced 1.2 27°C. [ The s.v.p. of water at 77°C and 27°C respectively are 314 mmHg and 27 mmHg. Treat the air in the vessel as an ideal gas]
(c) The lengtn of a zinc rod at 23°C is 200 m. Calculate the increase in length of the rod when its temperature rises to 33°C. [ expansivity of zinc = 2.6 x 10\(^{-5}\) K\(^{-1}\)]
(d) Explain with there is no temperature change when a solid being heated changes into liquid at its melting point.
(a) Two differences between boiling and evaporation
| Boiling | Evaporation |
|---|
| Occurs at a fixed temperature (the boiling point) | Occurs at all temperatures |
| Takes place throughout the whole liquid (bubbles form within it) | Takes place only at the exposed surface of the liquid |
(b) New pressure in the vessel after cooling
At \(77^\circ\text{C}\ (350\,\text{K})\), total pressure = 1007 mmHg and s.v.p. of water = 314 mmHg, so the partial pressure of the dry air is:
\[ P_{\text{air}} = 1007 - 314 = 693\,\text{mmHg} \]
The air (ideal, constant volume) is cooled to \(27^\circ\text{C}\ (300\,\text{K})\):
\[ P'_{\text{air}} = 693\times\frac{300}{350} = 594\,\text{mmHg} \]
Adding the s.v.p. of water at \(27^\circ\text{C}\) (27 mmHg):
\[ P_{\text{total}} = 594 + 27 = 621\,\text{mmHg} \]
(c) Increase in length of the zinc rod
\[ \Delta L = L\,\alpha\,\Delta\theta = 200 \times (2.6\times10^{-5}) \times (33-23) \]
\[ \Delta L = 200 \times 2.6\times10^{-5} \times 10 = 0.052\,\text{m} \ (5.2\,\text{cm}) \]
(d) When a solid melts at its melting point, the heat supplied (the latent heat of fusion) is used entirely to break the bonds/forces holding the particles in the fixed solid lattice, not to increase their kinetic energy. Since temperature depends on the average kinetic energy of the particles, and this does not change while the solid is turning to liquid, the temperature stays constant until melting is complete.
