How Does Heat Addition Change the Temperature of an Ideal Gas?

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The discussion revolves around calculating the final temperature of an ideal monatomic gas after adding heat and performing work on it. The initial conditions include three moles of gas at 345 K, with 2114 J of heat added and 811 J of work done. The relevant equation for internal energy change is highlighted as ΔU = Q - W, where Q is heat added and W is work done. It is emphasized that for an ideal gas, the specific heat at constant volume (Cv) is 3R/2, linking internal energy change to temperature change. The conclusion drawn is that the temperature change can be determined using the relationship ΔU = nCvΔT.
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Homework Statement


Three moles of an ideal monatomic gas are at a temperature of 345 K. Then, 2114 J of heat are added to the gas, and 811 J of work are done on it. What is the final temperature of the gas?


Homework Equations





The Attempt at a Solution


I have a feeling I'm missing an equation. I thought the equation was U = Q - W but that won't help me here.
 
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keemosabi said:
[

The Attempt at a Solution


I have a feeling I'm missing an equation. I thought the equation was U = Q - W but that won't help me here.
How is U related to temperature? Hint: what is the specific heat of a monatomic gas at constant volume (where W = 0 so Q = U)?

AM
 
Doesn't it depend upon the gas?
 
keemosabi said:
Doesn't it depend upon the gas?
Not if it is an ideal gas, which this is. The specific heat is Cv = 3R/2 where R is the universal gas constant (units are J/mole K). Since, by definition, \Delta Q = nC_v\Delta T and \Delta U = \Delta Q for a constant volume process and since U is a function only of T, it follows that

\Delta U = nC_v\Delta T[/itex]<br /> <br /> regardless of the type of process.<br /> <br /> AM
 

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