FYKOS Year 36 Series 3 Problem 2 — heating in the cottage · FYKOS 36 #36.3.2

Physics · mechanics · thermodynamics

Problem

Danka arrived at her cottage in the middle of winter with only

T_1 = 12\,\mathrm{^\circ\mskip-2mu\mathup{C}}

indoors. So she lit a fire in the fireplace by using wood of heating value

Q_0 = 14.23\,\mathrm{MJ\cdot kg^{-1}}

. How much wood does she need to burn to heat the air inside to

T_2 = 20\,\mathrm{^\circ\mskip-2mu\mathup{C}}

? The cottage is in the shape of a rectangular cuboid with dimensions

a = 6\,\mathrm{m}

b = 8\,\mathrm{m}

and

c = 3\,\mathrm{m}

. A roof is in the shape of an irregular recumbent triangular prism with a height of

v = 1.5\,\mathrm{m}

, the upper edge of which is the axis of the cottage layout. The air occupies

87\,\mathrm{\%}

of the volume of the cottage and its specific heat capacity is

c_{\mathrm{a}} = 1~007\,\mathrm{J\cdot kg^{-1}\cdot K^{-1}}

. Does the result match the expectation? Discuss the simplicity of the model used.