For an external wall of area a builder is considering two insulating materials

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

For an external wall of area 50 m250\,\text{m}^{2} a builder is considering two insulating materials, each to be supplied in a uniform layer 5.0 cm5.0\,\text{cm} thick. Material A: glass wool, kA=0.040 W m−1 K−1k_{A}=0.040\,\text{W\,m}^{-1}\,\text{K}^{-1}; Material B: expanded polystyrene, kB=0.030 W m−1 K−1k_{B}=0.030\,\text{W\,m}^{-1}\,\text{K}^{-1}. Throughout the heating season the temperature difference between the inner and outer wall surfaces may be taken as 18 K18\,\text{K}. Electricity costs Rs 6.06.0 per kWh and the heating system runs continuously for 200200 days each year. (a) For each material calculate the rate of heat transfer through the insulated wall. (b) Determine the corresponding electrical energy lost per day for each case. (c) Find the annual saving in energy cost if Material B is chosen instead of Material A. (d) If Material B costs Rs 8080 more per square metre than Material A to install, estimate the pay-back period for the additional investment.

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