When you crush a can with pressure by boiling some water inside thecan and the p
ID: 1738084 • Letter: W
Question
When you crush a can with pressure by boiling some water inside thecan and the putting it upside down in cold water, could you guyselaborate the physics happening with the Ideal Gas Law that crushesthe can?Please include an in depth explanation ofthe process, including formulas, pressure and/or temperaturechanges, approximations.
All input is welcome thanks!
Explanation / Answer
In the standard experiment, about {18 ml = 18 g = 1 mole} ofliquid water are placed in a {V = 0.5 L} can and heated to a temperatureof {T = 100 degC = 373.15 degK}. The water boils, and hot watervapor fills the can (and drives out any dry air). Thus: P*V = n*R*T ----> {# Moles H2OVapor In Can} = n = P*V/(R*T) ----> n = (1 atm)*(0.5 L)/((0.08206)*(373.15degK)) ----> n = 0.016328 mol The can is now inverted in cold water, so the can and enclosedwater vapor are cooled. Approx 99% of the water vapor condensesback to liquid inside the can, leaving only 1% of original moles of watervapor in the can volume: {# Moles H2O Vapor In Can AfterCooling} = (n_new) = = (0.01)*n = 0.00016328 mol Thus, new pressure (P_new) inside can after invertingand cooling to new temperature {(T_new) = 290 degK} is: P*V = n*R*T ----> (P_new) = (n_new)*R*(T_new)/V = = (0.00016328 mol)*(0.08206)*(290 degK)/(0.5 L) = 0.007771 atm = 787.42 Pa = (P_inside) ----> {Total Force OnCan Sides} = F = = {Pressure Diff Between Inside & Outside Can}*{CanArea} = ( (P_outside) -(P_inside) )*{h*(2*Pi*r)} = ( (101325 Pa) -(787.42 Pa) )*(0.2 m)*(2*Pi*(0.03m)) = 3790 N = {Equiv To 850 Pounds Placed On Can} The equivalent of an 850 pound weight placed on can surface willcertainly crush the can. .
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