Chapter 21, Problem 53A

People in the pioneering days placed hot potatoes in their pockets on cold winter days to keep their hands warm. Assuming that a potato is mostly water, Andrew calculates 24,000 calories of heat are released by a 350-g potato that cools from $85°C$ to $15°C$. Alexis calculates that 102,000 joules of heat are released. Whose answer do you agree with, and why?

To determine

To identify: The person that has done the heat released calculation correctly

Answer to Problem 53A

The heat released calculation done by both the persons are correct as the heat released is approximately equal to $24000\text{ calories or 102000 J}$ .

Explanation of Solution

Given:

The mass of potato is $m=350\text{ g}$ .

Consider the potato is cooled from $85°\text{C}$ to $15°\text{C}$ .

Formula used.

The expression for heat transfer is,

  $Q=mc\Delta T$

Here, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the temperature change.

Calculation:

Consider the specific heat as $c=1.0\text{cal}/\text{g°C}$ .

The change in temperature is,

  $\begin{array}{l}\Delta T=85°\text{C}-15°\text{C}\\ \Delta T=70°\text{C}\end{array}$

The amount of heat released a potato is,

  $\begin{array}{l}Q=mc\Delta T\\ Q=\left(350\text{ g}\right)\left(1.0\text{cal}/\text{g°C}\right)\left(70°\text{C}\right)\\ Q=24500\text{ calories}\times \frac{4.186\text{ J}}{1\text{ cal}}\\ Q=102557\text{ J}\end{array}$

The amount of heat released by a potato is approximately $24000\text{ calories or 102000 J}$ .

Conclusion:

Thus, the heat released calculation of both the persons are correct