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

Question

Quizplus · Accepted Answer

To find the time, use the formula: $ Q = mc\Delta T $ and $ P = \frac{Q}{t} $. Convert 1 liter of water to 1000 g, and the temperature change from 10°C to 30°C is 20°C. So, $ Q = 1000 \times 1 \times 20 = 20000 $ cal. Convert to joules: $ 20000 \times 4.18 = 83600 $ J. With power $ P = 400 $ W, $ t = \frac{83600}{400} = 209 $ s, which is approximately 3.5 minutes.

The Mechanical Equivalent of Heat Is 1 Cal = 4 °\degree°

The Mechanical Equivalent of Heat Is 1 Cal = 4 $\degree$