Starting with 2.50mol of N2 gas (assumed to be ideal) in a cylinder at 1.00 atm

Question

Starting with 2.50mol of N2 gas (assumed to be ideal) in a cylinder at 1.00 atm and 20.0 C, a chemist first heats the gas at constant volume, adding 1.36 X 10^4 J of heat, then continues heating and allows the gas to expand at constant pressure to twice its original volume.

(A) Calculate the final temperature of the gas. (Book Answer says: 837 C)

(B) Calculate the amount of work done by the gas. (Book Answer says: 11.5 kJ)

(C) The amount of heat added to the gas while it was expanding. (Book Answer says: 40.3 kJ)

(D) The change in internal energy of the gas for the whole process. (Book Answer says: 42.4 kJ)

I cannot get these answers, thank you for the help.

Explanation / Answer

Answer: According to the question , Here we have to use the equation ,

PV=nRT => U=Q-W => U=nCvT

Hence we, get : The first part suggests that the system is in a constant volume. Thus: U=Q

nCvT=Q

Now , putting all the values we get , 2.5 * 5/2 * R * [Tf -20 ] = 1.36 * 104

Tf = 261.7272 0C

means = 534.7272 Kelvin

Now the next part suggests the system is at a constant pressure and the volume doubles. So I use PV=nRT where n, R and P are constant.
V1/T1 = V2/T2

1 / 534.7272 = 2 / T2

T 2 = 1069.4544 kelvin

Hence the final temperature 1069.4544 - 273 dgree celcius

Hence we get the 796.45 0C

Now It is all about the given question , Now you can solve all the required part easily .

Thank you :)

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