What is the pressure of a system when the temperature is increased from 425 Kelvin to 654 Kelvin; provided the pressure of the system is 175 kPa and the system is sealed to prevent any leakage of gas into or out of the system.
We know that n and V 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 V on the same side of the equation, obtaining
n R / V is constant and therefore so is P / T. If the temperature changes by a certain factor, the pressure must therefore change by the same factor.
So when the temperature changes from 425 Kelvin to 654 Kelvin, a factor of
the pressure will change to
Alternatively we can say that since P / T is constant, P1 / T1 = P2 / T2 so P2 = P1 / T1 * T2 = P1 * (T2 / T1). Thus the new pressure 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 V are constant so is the ratio P / T. Since then P1 / T1 = P2 / T2, P2 = P1 * (V2 / V1).
A more intuitive way of looking at this is to realize that whenever P / T is constant, it follows that if the temperature changes from T1 to T2 while pressure changes from P1 to P2, we must have (P2 / P1 ) = (T2 / T1). That is, the pressure and volume ratios are equal.
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