Radiator · Estonian PhO 2018 #3

Physics · thermodynamics

Problem

In the room there is a water radiator with a nominal power Pn=\SI2.0kWP_{n}=\SI{2.0}{kW}. What is the actual power of this radiator and the temperature of the water flowing back? The speed of the heating water going through the radiator is q=\SI1.0l/minq=\SI{1.0}{l/min}, the temperature of the entering water is Tp=\SI70\degreeCelsiusT_{p}=\SI{70}{\degreeCelsius} and the room temperature is T0=\SI22\degreeCelsiusT_{0}=\SI{22}{\degreeCelsius}. How big is the maximal power of the radiator for the given temperatures? The specific heat of water is cw=\SI4200J/(kg⋅K)c_{w}=\SI{4200}{J/\left(kg\cdot K\right)} and the density ρw=\SI1000kg/m3\rho_{w}=\SI{1000}{kg/m^{3}}. Note. The nominal power of the radiator is its heating power for the fixed temperatures of the entering water (Tpn=\SI75\degreeCelsiusT_{pn}=\SI{75}{\degreeCelsius}), backflow water (Ttn=\SI65\degreeCelsiusT_{tn}=\SI{65}{\degreeCelsius}) and the room temperature (T0n=\SI20\degreeCelsiusT_{0n}=\SI{20}{\degreeCelsius}). Hint. You can assume that the actual power of the radiator is proportional to the difference between the average temperature of the entering and backflow water and the room temperature.

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