Chapter 14, Problem 1P

To what temperature will 8200 J of heat raise 3.0 kg of water that is initially at 10.0°C?

To determine

The temperature to which water will be raised when heated.

Answer to Problem 1P

Solution:

Water will rise to a temperature of ${10.6529}^o\text{C}$

Explanation of Solution

Given:

$Q$ is 8200 J

$cp$ of water is 4186 J/kgK

$m$ is 3 kg

$Tf$ is the final temperature to be determined

$Ti$ is 10 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:

Inserting the given values in the heat capacity formula:

$Q=mcp(Tf-Ti)$

$8200=(3)(4186)(Tf-10)$

$0.6529=(Tf-10)$

$Tf={10.6529}^o\text{C}$