Question

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.)

Answer 1

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 0^oC 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 = 0^oC = 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