Question

A canister filled with 1.3 mol of single-atom helium gas has a temperature of 315 K. What is the approximate total internal energy of the gas? (Recall that the equation for kinetic energy due to translation in a gas is: nRT; the2 equation for kinetic energy due to rotation of a molecule in a gas is: nRT; and R= 8.31 J/(mol-K).)A. 9500 JB. 5100 JC. 1200 JD. 4300 J

Answer 1

The total internal energy U of a monoatomic ideal gas is given by:

`U=(3)/(2)nRT`

Where n is the amount of substance, R is the universal gas constant and T is the temperature of the sample. The value of R is:

`R=8.314(J)/(mol\cdot K)`

Replace n=1.3mol and T=315K to find the internal energy of the gas:

`U=(3)/(2)(1.3mol)\left(8.314(J)/(mol\cdot K)\right)(315K)=5106.87...J`

Therefore, the approximate total internal energy of the gas is 5100J. The correct choice is Option B.