Hw #17

[Audrey Hanna]

Hi guys, I'm struggling with the second part of this problem: A 0.565 mol sample of Ar(g), initially at 298 K and 1.00 atm, is held at constant pressure while enough heat is applied to raise the temperature of the gas by 14.1 K. Calculate the amount of heat q required to bring about this temperature change, and find the corresponding total change in the internal energy ΔU of the gas. Assume that the constant‑pressure molar specific heat for Ar(g), which consists of single atoms, is equal to 5R/2, where R=8.3145 J/(mol·K) is the ideal gas constant.

I'm not sure how to solve for work in the equation ΔU = q+w, or maybe that's not the right equation at all?
Thanks!

[Ethan Crofut 1E]

Yes, you use deltaU = q + w.

First, you can immediately solve for q, since you are given the moles of gas (0.565), the constant-pressure molar specific heat (5R/2), and delta T (14.1 K).

Next you need to find w. In a constant pressure system, -(external pressure) * (deltaV) = w. You are already given external pressure is 1.00 atm. Use the ideal gas equation twice in order to solve for the initial and final volumes, using the initial temperature of 298 K for one, and the final temperature of 312.1 K for the other. Now you will have enough information to solve for work.

Then, plug into deltaU = q + w and that should give you the answer. One last thing to note, you will likely end up finding w in terms of L*atm, and they probably ask for the answer in J. 1 L*atm is 101.325 J.