Quantity of heat: If we use 67 W of power to heat 148 g of water, how long will it take to raise the temperature of the water from 15°C to 25°C? The specific heat of water is 4190 J/kg ∙ K.
A) 93 s
B) 5.3 s
C) 22 s
D) 114 h

Question

Quizplus · Accepted Answer

To calculate the time required to heat the water, we first find the amount of heat needed using the formula $Q = mc\Delta T$, where $m = 0.148 \, \text{kg}$ (since 148 g = 0.148 kg), $c = 4190 \, \text{J/kg} \cdot \text{K}$, and $\Delta T = 10 \, \text{K}$ (from 15°C to 25°C). Thus, $Q = 0.148 \, \text{kg} \times 4190 \, \text{J/kg} \cdot \text{K} \times 10 \, \text{K} = 6197.2 \, \text{J}$. The power $P = 67 \, \text{W}$ (or $67 \, \text{J/s}$) is used to deliver this energy, so the time $t$ can be found from $Q = Pt$, giving $t = Q / P = 6197.2 \, \text{J} / 67 \, \text{J/s} = 92.5 \, \text{s}$, which rounds to approximately 93 seconds.

Quantity of Heat: If We Use 67 W of Power