(a)(i) Sketch a graph to illustrate Charles' law. (ii) A gas occupies 500 cm\(^{ 3}\) at 2TC. calculate its volume at 40°C constant pressure. (b) List two g...

Answer Details

(a)(i) Charles' law states that at constant pressure the volume of a fixed mass of gas is directly proportional to its absolute (kelvin) temperature. A graph of volume against absolute temperature is therefore a straight line passing through the origin:

The line is straight and, when produced, passes through the origin (0 K, 0 cm\(^3\)), showing \(V \propto T\) at constant pressure. If the same volume is plotted against temperature in \(^{\circ}\)C, the straight line is displaced and cuts the temperature axis at \(-273\ ^{\circ}\text{C}\) (absolute zero).

(a)(ii) Convert both temperatures to kelvin:

\[T_1 = 27 + 273 = 300\ \text{K}, \qquad T_2 = 40 + 273 = 313\ \text{K}, \qquad V_1 = 500\ \text{cm}^3\]

At constant pressure, Charles' law gives:

\[\frac{V_1}{T_1} = \frac{V_2}{T_2} \quad\Rightarrow\quad \frac{500}{300} = \frac{V_2}{313}\] \[V_2 = \frac{500 \times 313}{300} = 521.7 \approx 522\ \text{cm}^3\]

The gas occupies 522 cm\(^3\) at 40 \(^{\circ}\)C.

(b) Two gases used as refrigerants:

• Ammonia (NH\(_3\))
• Carbon dioxide (CO\(_2\))