# Conclusion the temperature and volume of the gas are

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to expand. Conclusion: The temperature and volume of the gas are directly related to each other. As one increases, so does the other. Mathematically, the relationship between temperature and pressure can be represented as follows: V T or V = kT If the equation is rearranged, then... V T = k and, following the same logic that was used for Boyle’s law: V 1 T 1 = V 2 T 2 The equation relating volume and temperature produces a straight line graph (refer back to the notes on proportionality if this is unclear). This relationship is shown in figure 8.3. Volume 0 Temperature (K) Figure 8.3: The volume of a gas is directly proportional to its temperature, provided the pressure of the gas is constant. However, if this graph is plotted on a celsius temperature scale, the zero point of temperature doesn’t correspond to the zero point of volume. When the volume is zero, the temperature is actually -273.15 0 C (figure 8.4. A new temperature scale, the Kelvin scale must be used instead. Since zero on the Celsius scale corresponds with a Kelvin temperature of -273.15 0 C, it can be said that: Kelvin temperature (T) = Celsius temperature (t) + 273.15 133

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8.3 CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11 Volume (kPa) -273 C 0 C 0 K 273 K Temperature Figure 8.4: The relationship between volume and temperature, shown on a Celsius temperature scale. At school level, you can simplify this slightly and convert between the two temperature scales as follows: T = t + 273 or t = T - 273 Can you explain Charles’s law in terms of the kinetic theory of gases? When the temperature of a gas increases, so does the average speed of its molecules. The molecules collide with the walls of the container more often and with greater impact. These collisions will push back the walls, so that the gas occupies a greater volume than it did at the start. We saw this in the first demonstration. Because the glass bottle couldn’t expand, the gas pushed out the balloon instead. Exercise: Charles’s law The table below gives the temperature (in 0 C) of a number of gases under different volumes at a constant pressure. Volume (l) He H 2 N 2 O 0 -272.4 -271.8 -275.0 0.25 -245.5 -192.4 -123.5 0.5 -218.6 -113.1 28.1 0.75 -191.8 -33.7 179.6 1.0 -164.9 45.7 331.1 1.5 -111.1 204.4 634.1 2 -57.4 363.1 937.2 2.5 -3.6 521.8 1240.2 3.0 50.2 680.6 1543.2 3.5 103.9 839.3 1846.2 1. On the same set of axes, draw graphs to show the relationship between tem- perature and volume for each of the gases. 2. Describe the relationship you observe. 3. If you extrapolate the graphs (in other words, extend the graph line even though you may not have the exact data points), at what temperature do they inter- sect? 4. What is significant about this temperature? 134
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11 8.3 Worked Example 28: Charles’s Law 1 Question: Ammonium chloride and calcium hydroxide are allowed to react. The ammonia that is released in the reaction is collected in a gas syringe and sealed in.

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• Fall '10
• ALLISON

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