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**[SOLVED] Total translational kinetic energy**

**1.A 0.03m3 vessel contains helium (monatomic) gas at 0.0C and 1.00 atm. The total translational kinetic energy of the gas molecules is (in KJ).**

**2. 3/2KbT**

**3. pV=nRT**

where p is the pressure, V is the volume, n is the number of molecules present, R is the gas constant (8.31J/(mol*K)), and T is the temperature in Kelvins (273K = 0ºC)

The other equation is that the average translational kinetic energy K of a single molecule is

K = (3RT)/(2N)

where R and T are from the first equation and N is Avogadro's number (6.022E23).

Just sub in numbers:

K = (3 * 8.31 * 273) / ( 2 * 6.022E23) = 5.651E-21 Joules. This is the kinetic energy of one atom of helium at 0º C. Change the first equation around to get n = (pV) / (RT) and then multiply 5.65E-21 by n

where p is the pressure, V is the volume, n is the number of molecules present, R is the gas constant (8.31J/(mol*K)), and T is the temperature in Kelvins (273K = 0ºC)

The other equation is that the average translational kinetic energy K of a single molecule is

K = (3RT)/(2N)

where R and T are from the first equation and N is Avogadro's number (6.022E23).

Just sub in numbers:

K = (3 * 8.31 * 273) / ( 2 * 6.022E23) = 5.651E-21 Joules. This is the kinetic energy of one atom of helium at 0º C. Change the first equation around to get n = (pV) / (RT) and then multiply 5.65E-21 by n

The answer in the book shows its suppose to be 4.5kJ, but I'm yet to get that, I'm getting a way off number. Thanks for any help given :+)