A physicist is working with a closed system consisting of 3.33 moles of an ideal gas. Right now, the average kinetic energy of the gas molecules is 6.14 x 10–21. The physicist needs to raise the total internal energy of the system to 14,000 J without adding any heat.
In order to raise the internal energy to 14,000 J, the physicist must do how much work on the system? Round to two significant digits. (Remember, Boltzmann’s constant is , and the universal gas constant is 8.3145 J/K • mol.)

Question

A physicist is working with a closed system consisting of 3.33 moles of an ideal gas. Right now, the average kinetic energy of the gas molecules is 6.14 x 10–21. The physicist needs to raise the total internal energy of the system to 14,000 J without adding any heat.
 In order to raise the internal energy to 14,000 J, the physicist must do how much work on the system? Round to two significant digits. (Remember, Boltzmann’s constant is , and the universal gas constant is 8.3145 J/K • mol.)

anonymous · Answer

The average kinetic energy of the gas molecules is the energy that each molecule in the system has. So, our initial energy in the system is 6.14x10^(-21) times the number of molecules in the system (3.33 times Avogadro's number).

When we have that, we can get the difference between the initial energy, and the final energy. This is also the amount of work that would need to be done to the system to raise the internal energy to the desired point (assuming no heat transfer).