Question

loren has the samples of elements that are listed below at room temperature. he exposes the samples to the same heat source until each sample reaches a temperature of 90.0°c.
10 g of al(s) ($c_p$ = 0.897 j/(g·°c))
10 g of ag(s) ($c_p$= 0.234 j/g·°c )
10 g of fe(s) ($c_p$ = 0.450 j/g·°c)
10 g of zn(s) ($c_p$ = 0.387 j/g·°c )
from first to last, which lists the order in which these samples will reach 90.0°c?
○ al, fe, zn, ag
○ ag, zn, fe, al
○ al, fe, ag, zn
○ ag, al, zn, fe

Explanation:

Step1: Recall the heat formula

The heat required to raise the temperature of a substance is given by \( q = mC_p\Delta T \). Here, \( m \) (mass) is the same (10 g) for all samples, \( \Delta T \) (change in temperature) is the same (from room temperature to \( 90.0^\circ\text{C} \)), so \( q \) is proportional to \( C_p \) (specific heat capacity). A lower \( C_p \) means less heat is needed, so the sample will heat up faster (reach \( 90.0^\circ\text{C} \) first).

Step2: Order the \( C_p \) values

List the \( C_p \) values:

• \( \text{Ag: } 0.234 \, \text{J/(g·°C)} \)
• \( \text{Zn: } 0.387 \, \text{J/(g·°C)} \)
• \( \text{Fe: } 0.450 \, \text{J/(g·°C)} \)
• \( \text{Al: } 0.897 \, \text{J/(g·°C)} \)

Order from lowest to highest \( C_p \) (faster to slower heating): \( \text{Ag} < \text{Zn} < \text{Fe} < \text{Al} \). So the order to reach \( 90.0^\circ\text{C} \) is Ag (first), Zn, Fe, Al (last).

Answer:

B. Ag, Zn, Fe, Al