Many of you know the universal method of solving simple physics problems: you
have to find in a textbook an identity in which you know the values of all the
quantities except for one, substitute the numbers into this identity, and
calculate the unknown quantity.
This problem is even easier. You know right away that the identity needed for
its solution is the Clapeyron–Mendeleev equation for the state of an ideal
gas. This equation relates the pressure of an ideal gas p, the amount of substance n, the volume
occupied by the gas V, and the temperature T.
Given three of these quantities, you have to find the fourth quantity. Note
that the temperature of a gas and the volume occupied by it must always be
Each of the three input lines has the form “X = value”, where X is the
symbol for a physical quantity and value is a nonnegative integer not
exceeding 1000. The three lines specify the values of three different
quantities. Pressure is specified in pascals, amount of
substance in moles, volume in cubic meters, and temperature in kelvins. It is guaranteed that the
temperature and volume are positive. The universal gas constant R should be
taken equal to 8.314 J / (mol · K).
If the input data are inconsistent, output the only line “error”. If the
value of X can be determined uniquely, output it in the format “X =
value” with an accuracy of 10−3. If it is impossible to uniquely determine
the value of X, output the only line “undefined”.
p = 1
n = 1
V = 1
T = 0.120279
Recall that Pa = N / m2 and J = N · m.
Problem Author: Benoît Paul Émile Clapeyron, Dmitri Mendeleev
Problem Source: XII USU Open Personal Contest (March 19, 2011)