The thermal energy of 1.0 mol of a substance is increased by 1.0 J. What is the temperature change if the system is (a) a monatomic gas, (b) a diatomic gas, and (c) a solid?

Question

Accepted Answer

Hi, everyone in this practice problem, we're being asked to calculate to decrease in temperature of an element. We'll have a refrigerator taking out 2.5 jules of heat energy from a four moles of an element. We're being asked to calculate to decrease in the temperature of the element. If it is first neon, second oxygen and lastly third, a solid element. The options given are a 1st 0.5 Calvin, 2nd 0.3, Calvin and 3rd 0.0 25 Calvin B 1st 0.5 Calvin, 2nd 0.5 Calvin and lastly 3rd 0.5, Kelvin C 1st 0.8, Kelvin 2nd 0.3 Calvin and lastly 3rd 0.25 Calvin. And lastly D 1st 0.113, Kelvin 2nd 0.188 Kelvin and 3rd 15. Kelvin. So first, let's start with neon. So for the first part, we want to notice that neon is a mono atomic gas. So I'm just gonna write that down. First, neon is mono atomic. So that means the C P of neon will then be equals to three divided by two of R or 3.5, R where R is the universal ideal gas constant, where R is equals to 3.8 point jewels divided by ball Calvin just like. So, so calculating this, the CV will then be equals to three divided by two or 3.5, multiplied by 8.314, Joel divided by mole Kelvin. And that will give us the CV value of 12.47 Jules per mole Kelvin. Now solving for delta T for neon or for this mono atomic gas. Delta T will then be equals to delta E T H divided by N multiplied by CV. We want to substitute all of the known information that we have in the problem statement. The delta E T H is 2.5 joules N is given to be four moles and the CV is 12.47 Jules divided by Mole Kelvin, which is the one that we just calculated. So calculating this, our delta T value will then come out to a value of 0.5 Kelvin. So the decrease in the temperature of the element, if it is neon is going to be 0.5, Kelvin. Now moving on to the second part which is oxygen. So oxygen is going to be diatomic. So for oxygen, the CV will then be equal to 5.5 or five divided by two of R, the R is still 8.314. So five divided by two of R will be five divided by two, multiplied by 8. per mole Kelvin. And calculating this, the CV value will then equals to 20.79 Joel per mole Kelvin. So calculating the delta T, which will be equals to delta E T H divided by N CV. The delta E T H will be 2.5 chills and will be four moles. And the CV will be 20.79 Joles divided by mole Kelvin, which is just the one that we just found. And that will give us a delta T value of 0. Kelvin. So the decrease in the temperature of the element if it is oxygen is 0.3, lastly, we have a solid and the CV for the solid uh for a solid is going to equal to 25 Joles per mole Kelvin. So delta T will be equals to delta E T H divided by M CV, just as usual. And that will give us 2.5 Joles divided by four more multiplied by 25 shows per mole Kelvin. And that will give us the delta T value of 0.25 Kelvin. So the decrease in the temperature when it is neon when the element is neon is going to be 0.5 Kelvin and the decrease in the temperature when it is oxygen will be equals to 0.3 Kelvin. And when it is solid will equals to 0.25 Kelvin. So this will correspond to option A in our answer choices. So option A will be the answer to this particular practice problem. So that will 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. But other than that, that will be it for this one. Thank you.

The thermal energy of 1.0 mol of a substance is increased by 1.0 J. What is the temperature change if the system is (a) a monatomic gas, (b) a diatomic gas, and (c) a solid?

Verified Solution

Key Concepts

Heat Capacity

Degrees of Freedom

Specific Heat