Question

On a cold winter day where the outside temperature is -10o C, a heat pump provides 20 kW to heat a house to 20o C. The heat pump has a COPHP of 4 at the maximum power. The next day a storm brings the outside temperature down to −15o C. If the ratio of COPHP and the reversible COPrev for day 1 and day 2 is the same, COPHP for both days is the same, and that the house loses heat to the outside air, extrapolate the temperature of the house on the second day. (Hint: use ratio of COPHP and COPHP,rev for both days).

Answer 1

Calculation for finding out temperature of the house on the second day is done below.

= 263 K. Day ! Outside temperature, Tu = -10°C House temperature, THI = 20°C = 293 K. Heat provided by the heat pump to the house, Q,= 20 kkl. COP of heat pump on day I , COP, = 4. Day 2 : outside temperature, TL2 = -15°C = 258 K. House temperature, The = ? (To find) HPI CONDITIONS: # Ratio of COP and the reversible copper for day, and day 2 is the came. HP COPHP COP. HP COPHOI COP HP 2 COP COP rer COPgueri هو "rer 2 2 → Equ@ # COP HP for both days is the same. Equ 6 COPHPI COP. 'HP 2 SOLUTION Equ @ СОР, HPI COP HP 2 COP mert COPguera COP rera COPHP2 x Copeeri COP CAP COP rer 2 colouer fas Cortiva = COPARI by equ@ Tha THI THI-Tu TH2-TL Tug 293 293 - 263 TH2 - 258 TH2 THz - 258 293 30 30 TH2 = 293 TH2 – 258 (293) 258 (293) = (293 – 30) TH2 TH2 287.43 K = 14.43 °C Temperature of house on the second day = 14.43€ ANSWER:

Note:

• y°C= (273+y) K
• COPrev for heat pump= TH / (TH - TL), where TH=temperature of the space to which heat pump is to deliver the heat and TL=temperature of the space from which heat pump is absorbing the heat.