A picture window has dimensions of 1.40 m×m×2.50 mm and is made of glass 5.80 mm thick. On a winter day, the outside temperature is -16.0 ∘C

Question

A picture window has dimensions of 1.40 m×m×2.50 mm and is made of glass 5.80 mm thick. On a winter day, the outside temperature is -16.0 ∘C∘C , while the inside temperature is a comfortable 20.5∘C. while the inside temperature is comfortable 19.5 degree C.

a. At what rate is heat being lost through the window by conduction?
b. At what rate would heat be lost through the window if you covered it with a 0.750 mm thick layer of paper ( thermal conductivity 0.0500 W/m.K).

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Eirian 5 months 2021-08-29T20:54:54+00:00 1 Answers 6 views 0

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    2021-08-29T20:56:13+00:00

    Answer:

    a.1.762\times10^4W

    b.8.517\times 10^3W

    Explanation:

    a.Given T_C=-16.0\textdegree C, \ T_H=20.5\textdegree C, K_b_r_a_s_s=0.8W/m.K\\

    #To calculate the rate at which heat is being lost by conduction, we first calculate thermal resistance:

    R=K/L\\\\=\frac{5.8\times10^-^3}{0.8W/m.K}\\=7.25\times 10^-^3m^2.K/W

    #The rate of heat loss can be determined from the equation:

    H=\frac{A}{R}[T_H-T_C]\\\\=\frac{1.4m\times 2.5m\times(20.5--16.0)K}{7.25\times10^-^3m^2.K/W}

    =1.762\times10^4W

    Hence, the rate of heat loss through the window by conduction is 1.762\times10^4W

    b.Given that thermal conductivity is 0.0500W/m.K and L_p_a_p_e_r=0.075cm

    #After covering the window with the paper, there will be additional thermal resistance:

    R_t=R_g_l_a_s_s+R_p_a_p_e_r\\\\R_p_a_p_e_r=\frac{7.5\times 10^-^4M}{0.05W/m.K}\\\\=0.015m^2.K/W

    #To calculate the rate of heat loss if window is covered,R_t

    H=\frac{A}{R}[T_H-T_C]\\\\=\frac{1.4m\times2.5m\times[20.5--16.0]}{0.015m^2.K/W}\\\\=8.517\times 10^3W

    #The rate of heat loss when the window is covered is 8.517\times 10^3W

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