The initial temperature of a system is 141 Kelvin. As temperature of a system changes the volume changes from 385 liters to 779 liters. If the system is sealed and held at constant pressure, then what is the final temperature of the system?
We know that n and P are constant for this situation; R is a universal constant--constant for any situation. Starting with PV = nRT we rearrange to get the constant terms n, R and P on the same side of the equation, obtaining
n R / P is constant and therefore so is V / T. If the volume changes by a certain factor, the temperature must therefore change by the same factor.
So when the volume changes from 141 liters to 779 liters, a factor of
the temperature will change to
Alternatively we can say that since V / T is constant, V1 / T1 = V2 / T2 so T2 = V2 / V1 * T1 = T1 * (V2 / V1). Thus the new temperature is
Note that temperatures must be in absolute units--i.e., in degrees from absolute zero. Using Celsius temperatures with the Gas Laws is always a fatal error.
If PV = n R T, then if n and P are constant so is the ratio V / T. Since then V1 / T1 = V2 / T2, T2 = T1 * (V2 / V1).
A more intuitive way of looking at this is to realize that whenever V / T is constant, it follows that if the volume changes from V1 to V2 while temperarture changes from T1 to T2, we must have (V2 / V1 ) = (T2 / T1). That is, the temperature and volume ratios are equal.
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