Chapter 14, Problem 3P

To determine

Energy needed to maintain skin temperature

Answer to Problem 3P

Solution:

Energy needed to maintain skin temperature of 35 C $=0.04\text{candy bars}$

Explanation of Solution

Formula Used:

The formula used is the relation between temperature and specific heat from thermodynamics

$Q=mcp(Tf-Ti)$

Where,

$Q$ is the heat transferred

$cp$ is the specific heat

$m$ is the mass

$Tf$ is the final temperature

$Ti$ is the initial temperature

Given:

$Q$ is thermal energy to be determined

$cp$ of water is 4186 J/kgK

$m$ is mass of water

$\rho$ is density of water is1000 kg/cu.m

$A$ is surface area of water body which is 1 sq. m

$t$ is thickness of water body which is 0.5 mm or $0.5({10}^{-3})$ m

$Tf$ is 35 C

$Ti$ is 10 C

Calculation:

The mass of water $m$ is determined by the multiplying density $\rho$ with volume $v$

$m=\rho v$

Volume $v$ is given by multiplying area $A$ with thickness $t$

$v=At$

Now the mass becomes:

$m=\rho At$

Substituting the values,

$m=(1000)(1)(0.5({10}^{-3}))$

$m=0.5$ kg

Inserting the given values in the heat capacity formula: $Q=mcp(Tf-Ti)$

$Q=(0.5)(1.0{\text{kcal/kgC}}^{\text{ο}})(35-10)$

$Q=12.5\text{kcal}$

$=12.5(\frac{1}{300})\text{candy bars}$

$=0.04\text{candy bars}$