A closed container is filled partially by water. Rest of the volume contains n=

Question

A closed container is filled partially by water. Rest of the volume contains n= 10 moles of a mono-atomic ideal gas with molar heat capacity Cv=12.47 J/(mol K) at a pressure Po=1.03 105 (Pa) and temperature T=293 K. Amount of heat Q = 20000 Joules will be introduced into the gas by a heater.
Find change of temperature and the pressure after heating; (neglect any variation of gas volume) and Find the velocity of the water ejected from a pipe 10 meters below the water level after heating. Neglect the velocity of the water at the top.

Explanation / Answer

20000 Joules
20000/12.47 J/Mol
1603 mol Kelvin / 10 moles
160.3849238 degrees changes
160.38+273=433.3849238 Kelvin
P1/P2=T1/T2

1.03*10^5/x=273/433.3849238

x=1.63511*10^5 Pa

change=1.63511*10^5-1.03*10^5=6.0511*10^4 Pa 

1/2(p)v^2+ P2=P1+pgh

500v^2+1.03*10^5=1.63511*10^5+1000*9.81*10

500v^2=158611.528

v=17.81075675

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