Question

the specific heat of a certain type of cooking oil is 1.75 j/(g·°c). how much heat energy is needed to raise the temperature of 2.65 kg of this oil from 23 °c to 191 °c? q =

Explanation:

Step1: Convert mass from kg to g

Since \(1\ kg = 1000\ g\), for \(m = 2.65\ kg\), we have \(m=2.65\times1000\ g = 2650\ g\).

Step2: Calculate the temperature change

The formula for temperature change is \(\Delta T=T_{final}-T_{initial}\). Given \(T_{initial}=23^{\circ}C\) and \(T_{final}=191^{\circ}C\), then \(\Delta T=191 - 23=168^{\circ}C\).

Step3: Use the heat - energy formula

The formula for heat energy is \(q = mc\Delta T\), where \(c = 1.75\ J/(g\cdot^{\circ}C)\), \(m = 2650\ g\), and \(\Delta T=168^{\circ}C\).
Substitute the values into the formula: \(q=(2650\ g)\times(1.75\ J/(g\cdot^{\circ}C))\times(168^{\circ}C)\).
First, \(2650\times1.75 = 4637.5\), then \(4637.5\times168=789100\ J\).

Answer:

\(789100\)