Chapter 14, Problem 9P

An automobile cooling system holds 18 L of water. How much heat does it absorb if its temperature rises from 15°C to 95°C?

To determine

Heat absorbed in an automobile cooling system.

Answer to Problem 9P

Solution:

Heat absorbed in an automobile cooling system is 6027840 J.

Explanation of Solution

Given:

$Q$ is to be determined

$cp$ of water is 4186 J/kgK

$m$ is mass

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

$V$ is volume which is 18 L

$Tf$ is 95 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

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 18 L. 1000 L is 1 cu.m. So18 L is 0.018cu.m.

Mass is now

$m=(1000)(0.018)$

$m=18$ kg

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

$Q=(18)(4186)(95-15)$

$Q=\text{6027840}$ J