1. (a) Translate the following into a mathematical statement: “For an ideal gas
ID: 3028740 • Letter: 1
Question
1. (a) Translate the following into a mathematical statement: “For an ideal gas at constant pressure, it is known that the volume of the gas V, is directly proportional to the temperature of the gas T (in Kelvin).
(b) If a certain gas has a volume of 1.8 cubic meters at a temperature of 225 Kelvin, find the constant k and write the mathematical model that relates the V and K.
(c) Use your model from (b) to find the temperature of the gas if the volume increases to 2.6 cubic meters. Show all work.
Explanation / Answer
1) a volume of gas V is directly proportional to temperatute T
in mathematical stantement it can be written as
V = k T
where , k is the proportionality constant
b) b) volume = 1.8 cu metres
temperature = 225 kelvin
therefore, plugging the values in the formula we get
V = k T
1.8 = k * 225
k = 1.8 / 225 = .008
k = .008
c) if volume increases to 2.6 cubic metres
2.6 = .008 * T
T = 2.6 / .008 = 325 Kelvin
temperature = 325 Kelvin
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