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

Question

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

Quizplus · Accepted Answer

To calculate the time, use the formula $Q = mc\Delta T$, where $Q$ is the heat energy, $m$ is the mass, $c$ 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 $\Delta T = 25 - 15 = 10 \, ^\circ\text{C}$. Thus, $Q = 0.114 \cdot 4186 \cdot 10$. The power $P = 67.0 \, \text{W} = 67.0 \, \text{J/s}$, and time $t = Q / P$. Substituting the values and solving gives $t \approx 71 \, \text{s}$.

In a Flask, 114 15∘C to 25∘C?15 ^ { \circ } \mathrm { C } \text { to } 25 ^ { \circ } \mathrm { C } ?15∘C to 25∘C?

In a Flask, 114 $15 ^ { \circ } \mathrm { C } \text { to } 25 ^ { \circ } \mathrm { C } ?$