Question

# One mole of nitrogen gas confined within a cylinder by a piston is heated from 0°C...

One mole of nitrogen gas confined within a cylinder by a piston is heated from 0°C to 852°C at 1.00 atm.

(a) Calculate the work of expansion of the gas in joules (1 J = 9.87 × 10−3 L·atm). Assume all the energy is used to do work. (Enter your answer in scientific notation.)

(b) What would be the temperature change if the gas were heated with the same amount of energy in a container of fixed volume? (Assume the specific heat capacity of N2 is 1.00 J/g·K.)

SOLUTION:

(A) Work (W) = PΔV

P = pressure, ΔV = change in volume = V2 - V1

V1 = 22.4L because 1mol of gas at STP has volume of 22.4L. Gas is initialy at 0oC and 1atm i.e, at STP

P1V1 / T1 = V2P2/T2

V2 = V1 X T2 / T1 Because P1 = P2 = 1atm, T1 = 0C = 273K , T2 = 852C = 1125K

V2 = 22.4 L X 1125K / 273K = 92.30L

W = PΔV = 1atm X (92.3 - 22.4) = 69.9Latm = 69.9Latm / 9.87 × 10−3 = 7.08 X 103 J

(B) If the same energy is supplied to 1 mol of N2 the temperature will rise and can be calculated as:

Q = mcΔT

Q = heat supplied , m = mass of gas = 28g, c = specific heat = 1.00 J/g·K, ΔT = rise in temperature = T2 - T1

T1 = 0oC = 273 K, T2 = ?

7.08 X 103 J = 28 X 1 X (T2 - 273)

(T2 - 273) = 7.08 X 103 J / 28 = 252.85

T2 = 252.85 + 273 = 525.85K

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