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) ( = 0.897 J / (g°C)) 10 g of Ag (s) ( = 0.234 J/gi°C) 10 g of Fe (s) ( = 0.450 J/gi°C) 10 g of Zn (s) ( = 0.387 J/g°C) From first to last, which lists the order in which these samples will reach 90.0°C?

Ag (s), Zn (s), Fe (s), Al (s).

Explanation:

Specific heat capacity is defined as the amount of heat energy required to raise the temperature of a substance per unit of mass. In the problem, you have specific heat of each sample:

Al (s) = 0.897 J / (g°C)

Ag (s) = 0.234 J / (g°C)

Fe (s) = 0.450 J / (g°C)

Zn (s) = 0.387 J / (g°C)

As the mass of the samples is the same, the compound that reach first the temperature is the one with less specific heat capacity. Thus, order is:

Ag (s), Zn (s), Fe (s), Al (s).

Ag>Zn>Fe>Al

Explanation:

Step 1: Data given

Final temperature = 90.0 °C

10 g of Al (s) ( = 0.897 J / (g°C))

10 g of Ag (s) ( = 0.234 J/g°C)

10 g of Fe (s) ( = 0.450 J/g°C)

10 g of Zn (s) ( = 0.387 J/g°C)

Suppose the initial temperature is 0 °C

Step 2: Calculate the heat needed to heat

Q = m*C*ΔT

⇒with Q = the heat needed to heat the elements

⇒with m = the mass of the sample = since the mass is the same for each sample, this will not affect

⇒with c = the specific heat of the sample = the heat needed to raise 1 gram of the sample 1°C

⇒ΔT = the change of temperature = since all of the sample have the same initial and final temperature, this will not affect.

The sample with the lowest specific heat capacity will reach 90.0 °C the first

10 g of Ag (s) will heat the fastest

10 g of Zn (s)

10 g of Fe (s)

10 g of Al (s)

Ag>Zn>Fe>Al