Using the following expression and the fact that T f for liquid N 2 is 77K and r

Question

Using the following expression and the fact that Tffor liquid N2 is 77K and room temperature is 300K, whatreduction in volume would be expected when the air filled balloonis subjected to liquid nitrogen? (Assume constant pressure)PiVi/Ti =PfVf/Tf

Would all gases produce the same reduction in volume? Help! Having a hard time understanding the math. Using the following expression and the fact that Tffor liquid N2 is 77K and room temperature is 300K, whatreduction in volume would be expected when the air filled balloonis subjected to liquid nitrogen? (Assume constant pressure)PiVi/Ti =PfVf/Tf

Would all gases produce the same reduction in volume? Help! Having a hard time understanding the math.

Explanation / Answer

1.Because the process ocurs at constant pressure  Pi=Pf , the expresion reduces to:Vf/Vi = Tf/Ti 2. your not given an initial volume Vi so youhave to express Vf in terms of Vi  :    Vf =(Tf/Ti)Vi 3.(Tf/Ti ) equals the rate ofchange, for example if (Tf/Ti) = 0.5 [this is not thereal value] then you would say that the final volume is half the initialvolume, in other words the volume of the ballon was reduced inhalf. The expresion above is derived from Charles Law wich isexpected to be followed only by ideal gases but it is a goodaproximation to the behavior of real gases at high temperatures andlow pressure. 2. your not given an initial volume Vi so youhave to express Vf in terms of Vi  :    Vf =(Tf/Ti)Vi 3.(Tf/Ti ) equals the rate ofchange, for example if (Tf/Ti) = 0.5 [this is not thereal value] then you would say that the final volume is half the initialvolume, in other words the volume of the ballon was reduced inhalf. The expresion above is derived from Charles Law wich isexpected to be followed only by ideal gases but it is a goodaproximation to the behavior of real gases at high temperatures andlow pressure.

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