Chapter 14, Problem 8P

To determine

The time taken to heat cup of soup

Answer to Problem 8P

Solution:

Time taken to heat cup of soup is 167.44 seconds

Explanation of Solution

Given:

$P$ is 375 W

$cp$ of water is 4186 J/kgK

$m$ is mass

$\rho$ is density of water is 1000 kg/cu.m

$V$ is volume which is 250 mL or 250 L

$Tf$ is 75 C

$Ti$ is 15 C

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

Power formula:

$P=\frac{Q}{t}$

Where,

$P$ is the power

$t$ is time

Calculation:

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

with volume $V$

$m=\rho V$

Volume $V$ by the multiplying is 0.250 L. 1000 L is 1 cu.m. So 0.250 L is 0.00025 cu.m.

Mass is now

$m=(1000)(0.00025)$

$m=0.25$ kg

To find energy needed to raise the temperature of the soup, insert the given values in the heat capacity formula: $Q=mcp(Tf-Ti)$

$Q=(0.25)(4186)(75-15)$

$Q=62790$ J

The energy to heat the soup is $Q=62790$ J

Since power $P$ is 375 W

The time taken can be calculated using $P=\frac{Q}{t}$ by substituting the energy $Q=6279000$ J as power is energy delivered per unit time.

$P=\frac{Q}{t}$

$t=\frac{Q}{P}$

$t=\frac{62790}{375}$

$t=167.44$ seconds