2.0 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy.

a. Which gas has the higher initial temperature?

Question

2.0 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy.

a. Which gas has the higher initial temperature?

Accepted Answer

Hi, everyone in this practice problem, we are being asked to determine the gas with a greater initial temperature. We will have 3.2 moles of helium gas with an initial thermal energy of 1000 750 Joles brought into contact through a conducting boundary with 2.2 moles of Argan with an initial Permal energy of 12,100 Joles. We're being asked to state the guest with a greater initial temperature and the options given R A A gun with a greater initial temperature of 993. Kelvin, then helium of 98.7 Kelvin B argon with a greater initial temperature of 441. Kelvin. Then helium of 43.9 Kelvin C helium with a greater initial temperature of 441. Kelvin. Then ARGO of 43.9 Kelvin and lastly D helium with a greater initial temperature of 993. Kelvin. Then Argon of 98.7 Kelvin. So both helium and ARGO here are mono atomic gasses. The thermal energy of mono atomic gasses can be calculated by using E T H to be equal to three divided by two, multiplied by N multiplied by K B multiplied by T. At the same time E T H will equal to two divided by two multiplied by N R C. So we need to solve for T and solving for T using this last equation that we have T will then be equal to two multiplied by E T H divided by three, N R N is going to be the number of moles and R is the universal gas constant of R to be equal to 8.314 joles divided by mole Kelvin. So for helium guest, the helium will be equals two. We just let's just substitute off this value two E T H for helium H E divided by three N H E multiplied by R. So uh substituting the values from the problem statement, we have the E T H or the thermal energy of helium to be 1750 joles divided by three, multiplied by the number of moles, which is 3.2 moles of helium gas multiplied by R which is 8.314 jules divided by mole Calvin. And then doing this calculation, we get the temperature of helium to then be equal to 43.9 Kelvin just like. So now doing the same thing for our Ar we have temperature of Argan to be equals to two E T H of A R or Argan divided by three, multiplied by N A R multiplied by R substituting the values we have two multiplied by the thermal energy of A is given to be 12, uh 12,100 jules. So let's substitute that in divide that by three, multiplied by the end of A R or the moles of ARGO, which is 2.2 mole. And then multiply that with the um gas constant, which is 8.314 jules divided by mole. Kelvin. Calculating this, we will get the temperature of ARGO to be equals to Kelvin. So concluding this, we know that T A R or the temperature of ARGO is bigger or higher than the temperature of helium where the temperature of A is 441 Kelvin and the temperature of helium is 43.9 Kelvin. And that will correspond to option B in our answer choices. So answer B with Argon having a greater temperature of 441 Kelvin than helium of 43.9. Kelvin will be the answer to this particular practice problem and I'll be it for this video. If you guys still have any sort of confusion, please feel free to check out our adolescent videos on similar topics available on our website and I'll be it for this one. Thank you.

2.0 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy. a. Which gas has the higher initial temperature?

Verified Solution

Key Concepts

Thermal Energy

Temperature and Moles Relationship

Ideal Gas Law