# Speed kmh time mins 75 60 according to our definition

• JusticeIce1840
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Speed (km/h) Time (mins) 100 60 80 75 60 100 40 150 According to our definition, the two variables are inversely proportional is one variable is directly proportional to the inverse of the other. In other words, if we divide one of the variables by the inverse of the other, we should always get the same number. For example, 100 1 / 60 = 6000 If you repeat this using the other values, you will find that the answer is always 6000. The variables are inversely proportional to each other. 128

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CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11 8.2 We know now that the pressure of a gas is inversely proportional to the volume of the gas, provided the temperature stays the same. We can write this relationship symbolically as p 1 V This equation can also be written as follows: p = k V where k is a proportionality constant. If we rearrange this equation, we can say that: pV = k This equation means that, assuming the temperature is constant, multiplying any pressure and volume values for a fixed amount of gas will always give the same value. So, for example, p 1 V 1 = k and p 2 V 2 = k, where the subscripts 1 and 2 refer to two pairs of pressure and volume readings for the same mass of gas at the same temperature. From this, we can then say that: p 1 V 1 = p 2 V 2 In the gas equations, k is a ”variable constant”. This means that k is constant in a particular set of situations, but in two different sets of situations it has differ- ent constant values. Important: Remember that Boyle’s Law requires two conditions. First, the amount of gas must stay constant. Clearly, if you let a little of the air escape from the container in which it is enclosed, the pressure of the gas will decrease along with the volume, and the inverse proportion relationship is broken. Second, the temperature must stay constant. Cooling or heating matter generally causes it to contract or expand. In our original syringe demonstration, if you were to heat up the gas in the syringe, it would expand and force you to apply a greater force to keep the plunger at a given position. Again, the proportionality would be broken. Activity :: Investigation : Boyle’s Law Here are some of Boyle’s original data. Note that pressure would originally have been measured using a mercury manometer and the units for pressure would have been millimetres mercury or mm Hg. However, to make things a bit easier for you, the pressure data have been converted to a unit that is more familiar. Note that the volume is given in terms of arbitrary marks (evenly made). Volume Pressure Volume Pressure (graduation (kPa) (graduation (kPa) mark) mark) 12 398 28 170 14 340 30 159 16 298 32 150 18 264 34 141 20 239 36 133 22 217 38 125 24 199 40 120 26 184 1. Plot a graph of pressure (p) against volume (V). Volume will be on the x-axis and pressure on the y-axis. Describe the relationship that you see.
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• Fall '10
• ALLISON

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