Question

The specific heat capacity of aluminum is 900 J/kg°C. If heat is added to a sample ofaluminum at a rate of 1,071 W for 56 seconds and its temperature rises from 19°Cto 69°C, what is the mass of the aluminum? Express your answer in kg.

Answer 1

Given:

The specific heat capacity of aluminum is

$c\text{ = 900 J/kg }^{\circ}C$

The rate of heat flow is 1071 W.

The time is t = 56 s

The initial temperature is

$T_i=19^{\circ}C$

The final temperature is

$T_f\text{ = 69}^{\circ}C$

To find the mass of aluminum.

Explanation:

The mass of the aluminum can be calculated by the formula

$\begin{gathered} Rate\text{ = mc\lparen T}_f-T_i\text{\rparen} \\ m=\text{ }\frac{Rate}{c(T_f-T_i)} \end{gathered}$

On substituting the values, the mass will be

$\begin{gathered} m=\frac{1071}{900(69-19)} \\ =0.0238\text{ kg} \end{gathered}$

Thus, the mass of the aluminum is 0.0238 kg