Question

Calculate the minimum work needed to reduce the temperature of a 1.0-g block of copper form 1.10 K to 0.10 K, the surroundings being at 1.20 K. Proceed by supposing that the heat capacity remains constant at 39 m J K^-1 mol^-1 and that the coefficient of performance can be evaluated at the mean temperature of the block. Then go on to do a more realistic calculation in which Cp,m = AT³ + BT, with A = 48.2 m J K^-1 mol^-1 and B = 688 m J K^-1 mol^-1, and taking into account the variation of the coefficient of performance with temperature.

Answer 1

Rt = R f (t)

dt = 1 / Rt₁ ( dR /dt )_t1

dt = I / f (t₁) [ df (t) / dt ]t1

Temperature cofficient with copper

t₂ R t ₂ = Rt - Rt₂ / t - t ₂

Rt - Rt₂ ( I + I₂ (t - t₂ )

particular temperature = 1.0g

converted temperature = 6.75

variation coefficient factor and copper (76.2 - 7.52 )

Pv = nRT

vi = 50 cm³ = 50 m³

vf = 150 cm³= 150 m³

p = 101300

n = 0.007moles

R = 8.315 J

where u = 0 and H = 0

  u / H = H _m

= 18889J / mol