Question

Gas in a piston combusts at 4 atm constant. Inital temp is 27C and final temp is 202C, inital volume is 1.5L. what is the final volume?

My question is how do I manipulate the variables to arrive to my answer?

Answer 1

For an ideal gas, \(PV=nkT\) where P is pressure V is volume, and T is thermodynamic temperature (in Kelvin). We dont need to worry about n and K in this as they are constant, and we will just be interested in ratios.

Now, we are told that intialy the volume is 1.5 L at 27 C (= 300 K), at 1 atmosphere. This is before compression. After compression, the gas is 202 C (= 495 K), at 4 atmosphere.

If we label the parameters \(i\) and \(f\) for initial and final, we can formulate it as the following \[\frac{P_{i}V_{i}}{T_{i}}=constant=\frac{P_{f}V_{f}}{T_{f}}\]. Because both terms equal the same constant, we can equate the before and after variables directly. Thus plugging in the numbers in we get \[\frac{(1)\times (1.5)}{(300)}=\frac{(4) \times (V_{f})}{(495)}\] Rearranging we get that \[V_{f}=\frac{(1.5)\times (495)}{(4)\times(300)}=0.61875\textrm{ L}\]