Problem — Heat loss from a house

Problem

A house with $120$ m$^2$ of heat-loss surface has an overall thermal coefficient $U = 0{,}5$ W/(m$^2 \cdot$K) (good energy class). The inside room is at $20\,^{\circ}$C, the average winter outside temperature is $0\,^{\circ}$C. (a) What is the power lost, in W? (b) What is the energy lost per day, in kWh? (c) What is the annual cost over the cold season ($4$ months $\approx 120$ days), with a tariff of $0{,}25$ €/kWh?

The warm house loses a heat flow $\dot Q$ to the cold outside.

Solution

The temperature difference is $\Delta T = 20\,^{\circ}\text{C} - 0\,^{\circ}\text{C} = 20$ K.

(a) The power lost is: $\dot Q = U \, A \, \Delta T = 0{,}5 \cdot 120 \cdot 20 = 1200 \ \text{W}$

(b) In one day ($24$ h) the energy lost is: $E = 1200 \ \text{W} \cdot 24 \ \text{h} = 28800 \ \text{Wh} = 28{,}8 \ \text{kWh}$

(c) Over $120$ days of the cold season: $E_{\text{tot}} = 28{,}8 \cdot 120 = 3456 \ \text{kWh} \qquad \text{cost} = 3456 \cdot 0{,}25 \approx 864 \ \text{EUR}$

$\ev{\dot Q = 1200 \ \text{W}; \quad E = 28{,}8 \ \text{kWh/day}; \quad \text{cost} \approx 864 \ \text{EUR/year}}$

Collegamenti

Argomenti: Termologia Concetti: Trasmissione del calore