Three moles of an ideal monatomic gas expand at a constant pressure of 3.00 atm ; the volume of the gas changes from 3.40×10^-2 m^3 to 4.50×10^-2 m^3
Calculate the amount of heat added to the gas
pV = nRT
Cv = (3/2)R for a monatomic ideal gas
The Attempt at a Solution
Using pV = nRT I found that the initial temperature Ti = 414 K and Tf = 548 K.
Then I want to use the equation dQ = n(Cv)dT to solve for the amount of heat added in the system. The correct answer is 8360 J, but when I do:
3*(3/2)*R*(548-414) = 5010 J
I think my problem is coming from not understanding the difference between dT and [itex]\Delta[/itex]T, or dQ and [itex]\Delta[/itex] Q. I actually know Δ is just the change (final-initial), and the derivative is the infinitesimal rate of change, so perhaps I'm just trying the wrong formula since I don't have dT? Or is there a way to figure out dT from what I'm given?