Calculate the temperature rise of a mass due to energy transfer over time.

Specific question: The hot tub system has a volume of 4.5 m3 and is filled with water at a temperature of 28 °C. The heater transfers thermal energy to the water at a rate of 2.7 kW while a pump circulates the water. Assume that no heat is transferred to the surroundings. Calculate the rise in water temperature that the heater could produce in 1.0 hour. Density of water = 1000 kg m^-3 . Specific heat capacity of water = 4200 J kg–1 K–1We begin with the specific heat capacity equation: Energy = Mass x Specific heat capacity(S.H.C) x Tempchange. Rearranging for Temperature change we get: TempChange = Energy/ (Mass x S.H.C). We are given the S.H.C and so only need to obtain the mass and the energy.We can observe that the volume and density is given and using the equation Mass = Volume x Density , we can calculate the mass by doing 4.5 x 1000 = 4500Kg. Now we need energy. To do this we are given the power and time. Relating them by using Power = Energy/Time and hence Energy = Power x Time we can input the given values to arrive at 2.7 x 1000 x 3600 = 9720000J. Now we just input the values we have found into the equation for temperature change giving us:Temperature Change = 9720000 / ( 4500 x 4200) = 0.51 K. Throughout, make sure to check the units of the values used!Eg , Energy is in Joules. So Power must me in Joules per Second (Watts) and Time must therefore be in Seconds.This is why the power is multiplied by 1000 for example as kW is the unit for 1000 Watts and the Time is converted from 1 hour to 60 x 60 seconds = 3600 seconds.