If 0.500 mol neon at 1.00 atm and 273 K expands against a constant external pressure of 0.100 atm until the gas pressure reaches 0.200 atm and the temperature reaches 210 K, calculate the work done on the gas, the internal energy change, and the heat absorbed by the gas.

The work done on neon = - 323 J

The internal energy change = - 392.84 J

The heat absorbed by neon = - 69.84 J

Explanation:

Step 1: Data given

Number of moles = 0.500 moles

Pressure = 1 atm

Temperature = 273 Kelvin

The pressure will change from 1.00 atm to 0.200 atm. The temperature changes from 273 to 210 Kelvin.

a) calculate the work done on neon

W = - P (V2-V1)

⇒ with P = the pressure = 0.1 atm

⇒ with V1 = the initial volume = nRTi / Pi

⇒ with V2 = the final volume = nRTf / Pf

W = - PnR ((T2/P2) - (T1/P1))

⇒ with T2 = the final temperature = 210 K

⇒ with T1 = the initial temperature = 273 K

⇒ with P2 = the final pressure = 0.200 atm

⇒ with P1 = the initial pressure = 1.00 atm

W = - nR (210 * (0.1/0.2) - 273 * (0.1/1.00))

W = - nR * (105 - 27.3)

W = - (0.500) * (8.314) * (77.7)

W = - 323 J

b) calculate the internal energy change

E = (3/2) * nRT

ΔE = Ef - Ei

ΔE = (3/2) * nR (T2-T1)

⇒ with n = number of moles = 0.500 moles

⇒ with T2 = the final temperature = 210 K

⇒ with T1 = the initial temperature = 273 K

ΔE = (3/2) * (0.5) * (8.314) (210-273)

ΔE = - 392.84 J

c) Calculate the heat absorbed by neon

ΔE = q + W

q = ΔE - W

⇒ with ΔE = - 392.84 J

⇒ with W = - 323 J

q = - 392.84 J - (-323 J)

q = -392.84 J + 323 J

q = - 69.84 J