Please Help! Word Problem

Question

One way The Ideal Gas Law can be stated is: In a closed system with a constant volume, the the pressure exerted by the contained gas (measured in atmospheres) changes directly proportionally to temperature changes of the gas.

For a particular closed system, it is known that for every 19 degree increase (measured in celsius), the pressure exerted increases by 5.6 atmospheres.

If the gas is currently at a temperature of 21 degrees and the pressure is 8.84 atmospheres, what should the temperature be for this system if we want the pressure to be 7.336842 atmoshperes?

Answer 1

First of all, you need to come up with the constant of proportionality of the ratio of a change of pressure to a change in temperature in which is:

 

k = P/T = 5.6 atm/19 ^oC

 

Also, the constant of proportionality can be used in setting up a linear equation with temperature being the independent variable and pressure being the dependent variable in which is:

 

P - 8.84 = k*(T - 21)

 

Now substitute the given pressure in the equation to solve for the required temperature in which is:

 

7.336842 - 8.84 = 5.6/19*(T - 21)

 

Now, I'll leave it up to you to solve for the temperature, T.