Page:International Library of Technology, Volume 93.djvu/51

remaining at 60° throughout the whole operation, the final pressure may be found by the formula pv = p₁v₁. Thus,

40 × 4,875 = p₁ × 3

and p₁ = 40 × 4,875/3 = 65 lb. per sq. in

as before.

43. Mixture of Two Unequal Volumes of Gas Having: Unequal Pressures. — Let p₁ and v₁ be the pressure and volume, respectively, of one quantity of gas; p₂ and v₂ be the pressure and volume, respectively, of the other quantity of gas; and let P and V be the pressure and volume, respectively, of the mixture. Then, if the temperature remains constant,

$PV=p_{1}v_{1}+p_{2}v_{2}$ (1)

That is, if the temperature is constant, the volume, after mixture, multiplied by the resulting pressure, is equal to the volume of one quantity of gas, before mixture, multiplied by its pressure, plus the volume of the other quantity of gas multiplied by its pressure.

From this formula, by dividing both sides of the equation by V,

$P={\frac {p_{1}v_{1}+p_{2}v_{2}}{V}}$ (2)

and, dividing both sides of the equation by P,

$V={\frac {p_{1}v_{1}+p_{2}v_{2}}{P}}$ (3)

Example 1.— Two quantities of gas of the same temperature, having volumes of 6 cubic feet and 41/2 cubic feet, and pressures of 261/2 pounds and 18 pounds per square inch, respectively, are mixed together in a vessel whose volume is 10 cubic feet. The temperature of the two gases and of the mixture being the same, what is the resulting pressure?

Solution. — Using formula 2, and substituting the given values,

$P={\frac {26{\frac {1}{2}}\times 6+18\times 4{\frac {1}{2}}}{10}}={\frac {159+81}{10}}=24$ lb. per sq. in. (Ans.)

Example 2. — If the two quantities of gas in example 1 are mixed in a vessel in which the resulting pressure is 30 pounds, what is the volume of the vessel, the temperature of the two gases and of the mixture remaining the same?