Question

if the specific heat of chromium is 0.4491 j/g°c, what is the mass of a piece of chromium if it takes 36000 j of heat to raise the temperature from 240°c to 255°c?

Explanation:

Step1: Recall heat transfer formula

The formula relating heat, mass, specific heat, and temperature change is $Q = mc\Delta T$, where $Q$ is heat energy, $m$ is mass, $c$ is specific heat, and $\Delta T$ is temperature change.

Step2: Calculate temperature change

$\Delta T = T_{final} - T_{initial} = 255^\circ\text{C} - 240^\circ\text{C} = 15^\circ\text{C}$

Step3: Rearrange formula to solve for mass

Rearrange $Q = mc\Delta T$ to isolate $m$: $m = \frac{Q}{c\Delta T}$

Step4: Substitute values into formula

Substitute $Q=36000\ \text{J}$, $c=0.4491\ \text{J/g}^\circ\text{C}$, $\Delta T=15^\circ\text{C}$:
$m = \frac{36000}{0.4491 \times 15}$

Step5: Compute the result

First calculate denominator: $0.4491 \times 15 = 6.7365$
Then divide: $m = \frac{36000}{6.7365} \approx 5344$

Answer:

The mass of the chromium piece is approximately 5344 grams.