The time taken to heat the cup of soup. 167.44 s Given: The immersion heater is rated at power P = 375 W ≈ 375 J/s . The volume of the water is V = 250 mL . Assume the density of water as ρ = 1 g/mL . The initial temperature of the cup is T 1 = 15 ° C . The final temperature of the cup is T 2 = 75 ° C . Assume the specific heat of water is c = 4.186 J/g ° C . Formula used: Show the expression for the time ( t ) taken for heating the cup from temperature T 1 to T 2 as follows: P t = ρ V c T 2 − T 1 t = ρ V c T 2 − T 1 P Calculation: Find the time taken for heating the cup from temperature T 1 = 15 ° C to T 2 = 75 ° C as follows: t = ρ V c T 2 − T 1 P Substitute the values: t = 1 g/mL 250 mL × 4.186 J/g ° C 75 ° C − 15 ° C 375 J/s t = 62790 J 375 J/s t = 167.44 s Conclusion: Thus, the time taken for heating the cup from temperature 15 ° C to 75 ° C is 167.44 s .

(II) A small immersion heater is rated at 375 W. Estimatehow long it will take to heat a cup of soup (assume this is250 mL of water) from 15°C to 75°C.

(II) A water heater can generate 32000 KJ/h. How much water can it heat from 12°C to 42°C per hour?

(II) A certain car has 14.0 L of liquid coolant circulating at a temperature of 93°C through the engine's cooling system. Assume that, in this normal condition, the coolant com- pletely fills the 3.5-L volume of the aluminum radiator and the 10.5-L internal cavities within the aluminum engine. When a car overheats, the radiator, engine, and coolant expand and a small reservoir connected to the radiator catches any resultant coolant overflow. Estimate how much coolant overflows to the reservoir if the system goes from 93°C to 105°C. Model the radiator and engine as hollow shells of aluminum. The coefficient of volume expansion for coolant is ß = 410 × 10-6/C°.