Answer to Question #287083 in Mechanics | Relativity for lau

Question

n a cooling system, 50 litres of oil per hour are cooled from 120ᴼc to 25ᴼc by means of circulating water. if the water is not to rise in temperature by more than 6ᴼc, calculate the mass of water, in kilograms, required per hour. assume the oil to have a specific heat capacity of 2100j/kgᴼc and its density to be 880 kg/m³.

Answer 1

Determine the mass of water from the condition for thermal equilibrium:

$$Q_\text{oil}=Q_\text{water},\\ c_\text{oil}m_\text{oil}(t_\text{f. oil}-t_\text{i. oil})=c_\text{w}m_\text{w}\Delta t_\text{w},\\\space\\ m_\text{w}=\dfrac{c_\text{oil}m_\text{oil}(t_\text{f. oil}-t_\text{i. oil})}{c_\text{w}\Delta t_\text{w}},\\\space\\ m_\text{w}=\dfrac{c_\text{oil}V_\text{oil}\rho_\text{oil}(t_\text{f. oil}-t_\text{i. oil})}{c_\text{w}\Delta t_\text{w}},\\\space\\ m_\text{w}=348 \text{ kg}.$$