Chapter 14, Problem 10P

What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 4.1 kg of the metal from 18.0°C to 37.2°C?

To determine

The specific heat of a metal.

Answer to Problem 10P

Solution:

The specific heat of a metal is 1715 J/kgK

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 135kJ or 135000 J

$cp$ is to be determined

$m$ is 4.1 kg

$Tf$ is 37.2 C

$Ti$ is 18 C

Calculation:

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

$135000=(4.1)(cp)(37.2-18)$

$135000=(4.1)(cp)(19.2)$

$cp=1715$ J/kgK