The mechanical equivalent of heat is 1 cal = 4.18 J.The specific heat of water is 1 cal/g·K, and its mass is 1 g/cm³.An electric immersion water heater, rated at 400 W, should heat a liter of water from 10°C to 30°C in about: A)12 s B)50 s C)3.5 min D)15 min E)45 min

Question

Quizplus · Accepted Answer

The amount of heat required to raise the temperature of one gram of water by one degree Celsius is given by its specific heat, which is 1 cal/g·K. To heat one liter (1000 g) of water from 10°C to 30°C, we need:
Q = (1000 g)(1 cal/g·K)(30°C - 10°C) = 20,000 cal
To convert this to joules, we use the mechanical equivalent of heat:
1 cal = 4.18 J
20,000 cal = (20,000 cal)(4.18 J/cal) = 83,600 J
The electric immersion water heater is rated at 400 W, which means it can provide 400 J of energy per second (J/s). The time it takes to heat the water can be found by dividing the total energy required by the power of the heater:
Time = Energy/Power = 83,600 J/400 J/s = 209 s
This is approximately 3.5 minutes. Therefore, the correct answer is choice C.

The Mechanical Equivalent of Heat Is 1 Cal = 4