A glass windowpane in a home is 0.62 cm thick and has dimensions of 1.30 m × 2.22 m. On a certain day, the indoor temperature is 22°C and the outdoor temperature is 0°C. (Assume the thermal conductivity of the glass is 0.8 J/s · m · °C.)
What is the rate at which energy is transferred by heat through the glass?
(b) How much energy is lost through the window in one day, assuming the temperatures inside and outside remain constant?
To find the rate at which energy is transferred by heat through the glass, you can use the equation:
Q = k * A * ΔT / d
Where:
Q is the rate of energy transfer (in joules per second or watts),
k is the thermal conductivity of the glass (0.8 J/s · m · °C),
A is the surface area of the glass (1.30 m × 2.22 m),
ΔT is the temperature difference between inside and outside (22°C - 0°C = 22°C),
and d is the thickness of the glass (0.62 cm = 0.62/100 = 0.0062 m).
Substituting the values into the equation:
Q = 0.8 * (1.30 * 2.22) * 22 / 0.0062
Q ≈ 7775.48 watts or 7775.48 joules per second
To calculate how much energy is lost through the window in one day, you need to consider the time. Assuming a day consists of 24 hours (86400 seconds), you can find the total energy lost by multiplying the rate of energy transfer by the time:
Energy lost = Q * time
Energy lost = 7775.48 * 86400 joules
Energy lost ≈ 672,331,072 joules or approximately 672.33 megajoules
Therefore, the energy lost through the window in one day is approximately 672.33 megajoules, assuming the temperatures remain constant.