Starting with 2.80 mol of N2 gas (assumed to be ideal) in a cylinder at 1.00 atm

Question

Starting with 2.80 mol 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 × 104 J of heat, then continues heating and allows the gas to expand at constant pressure to twice its original volume.

Calculate the final temperature of the gas

Calculate the amount of work done by the gas.

Calculate the amount of heat added to the gas while it was expanding.

Calculate the change in internal energy of the gas for the whole process.

Explanation / Answer

1) calculation of final temperature

P1=1atm   V1 = V : T1 = 20 + 273 = 293K

P2 = P1(Constant): V2 = 2V: T2 = ?

Ideal gas V1/T1 = V2/ T2

   T2 = V2/V1 * T1 =

   = 2V/V * 293 =2 * 293 = 586 K

t2: 586-273=3130C

Calculation of amount of Work done:

W = R/(r-1) * (T2 -T1)

R =8.314 J/Mol/K

r = 1.4( 2 diatomic molecule)

T2 =586K

T1 = 293K

W = 8.314/(1.4-1) * (586-293)

= 8.314/(0.4) * (293)

= 8.314*2930/4 = 6090J

Calculate the change in internal energy of the gas dU = dQ-dW

= 1.36 * 104 - 6090

= 13600-6090 = 7510 J

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