Question

For an ideal monatomic gas, what happens to the internal energy of a system if the average molecular speed of the gas atoms doubles? ​Select only one.

a. The internal energy down by a factor of 2

b. The internal energy remains constant (independent of atom speed)

c. The internal energy goes up by a factor of 4

d. The internal energy goes up by a factor of 2

e. The internal energy down by a factor of 4

f. Unknown without more information

Answer 1

Answer : "c" the internal energy goes up by a factor of 4

Explanation: The internal energy of a thermodynamic system is the sum of the mechanical energies of all of the molecules in it. For a monoatomic ideal gas,the molecules only energy is their translational kinetic energy. Therefore

E_int = 3/2Nk_bT

But kineticenergy, K= 1/2mv² =3/2k_bT

So internal energy directly proportional to v^2

Given that average molecular speed of the gas atoms is doubled then the internal energy goes up by a factor of 4

Answer: c