What Celsius temperature of a closed and sealed system, held at constant pressure, will result in a volume of 291.5 liters if the volume of the system is 247 liters when the temperature is 257 Celsius?
The absolute temperature T is (273+ 257 ) K = 530 K. Note that it is always essential to use absolute temperatures with the gas laws.
Since n and P are constant, we algebraically rearrange PV=nRT to the form V/T = nR/P. Since the right-hand side is now constant (since each factor on this side is constant), we see that V/T is constant.
Thus, when T increases, V must increase in the same proportion (otherwise V/T would change).
If, as in the present example, V changes from 247 liters to 291.5 liters; the proportional change is
The new temperature will therefore be
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 temperature changes from T1 to T2 while volume changes from V1 to V2, we must have (V2 / V1 ) = (T2 / T1). That is, the volume and temperature ratios are equal.
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