Final answer:
Using Boyle's Law, which requires temperature to remain constant, we determine the final pressure after compression to be 4.25 atm. Since this is below the breakage point of 7.0 atm, the cylinder will not break.
Step-by-step explanation:
The gas law used for this problem is Boyle's Law, which states that for a given mass of an ideal gas at constant temperature, the volume is inversely proportional to the pressure (PV = k where k is a constant). Since the initial conditions of the gas in the cylinder are 400K and 2.0atms at 4.25L and we are told that the temperature remains constant, we can use Boyle's Law to figure out if the cylinder will break due to the pressure increase when the volume is compressed to 2L.
Initial conditions: P1 = 2.0 atm, V1 = 4.25 L.
Final conditions: V2 = 2.0 L (we need to find P2).
Applying Boyle's Law:
P1*V1 = P2*V2
2.0 atm * 4.25 L = P2 * 2.0 L
P2 = (2.0 atm * 4.25 L) / 2.0 L
P2 = 4.25 atm
The final pressure is 4.25 atm which is below the cylinder's breakage point of 7.0 atm. Therefore, the cylinder will not break under this compression.