In a flask,114.0 g of water is heated using $67.0 \mathrm {~W}$ of power,with perfect efficiency.How long will it take to raise the temperature of the water from $15 ^ { \circ } \mathrm { C }$ to $25 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat of water is 4186 J/kg ∙ K.

Question

Quizplus · Accepted Answer

To calculate the time required to heat the water, use the formula $Q = mc\Delta T$, where $Q$ is the heat energy in joules, $m$ is the mass in kilograms, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. Here, $m = 114.0 \, \text{g} = 0.114 \, \text{kg}$, $c = 4186 \, \text{J/kg} \cdot \text{K}$, and $\Delta T = 25 - 15 = 10 \, \text{K}$. So, $Q = 0.114 \cdot 4186 \cdot 10$. The power $P = 67.0 \, \text{W} = 67.0 \, \text{J/s}$, and time $t = Q / P$. Substituting the values and solving gives the time in seconds.

In a Flask,114 67.0 W67.0 \mathrm {~W}67.0 W Of Power,with Perfect Efficiency 15∘C15 ^ { \circ } \mathrm { C }15∘C

In a Flask,114 $67.0 \mathrm {~W}$ Of Power,with Perfect Efficiency $15 ^ { \circ } \mathrm { C }$