Question

The internal energy of 10 moles of helium (a monatomic gas) is 15 kJ. What is the rms speed of the molecules? (The molar mass of helium is 4.00 g/mole.)

Answer 1

Answer:

$v_{rms}=866.32m/s$

Explanation:

Hello,

In this case, since the rms speed of the molecules is computed by:

$v_{rms}=\sqrt{\frac{3RT}{M} }$

Whereas the absolute temperature is computed from the internal energy (by using the Cp of helium (3.1156 J/g*K) as shown below:

$U=nCvT\\\\T=\frac{U}{nCv}=\frac{15kJ*\frac{1000J}{1kJ} }{10mol*\frac{4.00g}{1mol} *3.1156\frac{J}{g*K} } \\\\T=120.36K$

Thereby, the rms speed results:

$v_{rms}=\sqrt{\frac{3*8.314\frac{kg*m^2}{s^2*mol*K}*120.36K}{4.00\frac{g}{mol}*\frac{1kg}{1000} } } \\\\v_{rms}=866.32m/s$

Regards.