Question

80 g of a diatomic ideal gas has a root-mean-square speed of 353 m/s. What is the internal energy of the gas?

Answer 1

Since In diatomic gases, there are Potential Energy also between the molecules alongwith the Kinetic Energy. Then its internal energy will be different from kinetic energy.

Root Mean Square velocity is given by ..................................(1)

where T= Temperature of the gas

R= Universal Gas Constant

M= Molar mass of the gas.

Now We know that Internal Energy of the Diatomic Gas is given by

  

where k= boltzmann constant, and

N_A= No. of molecules in 1 mole= Avogadro's number

T= Temperature of the gas.

Then we'll have

  ....................................(2)

where n= no. of moles of the gas,

Also we know that no. of moles is given by

where m= given mass of gas and

M= molar mass.

Then equation 2 will become,

  

Using equation 1 in above,

now using all given values in above,

    (ANS)