Question

Four substances at the same temperature absorb equal amounts of energy. The specific heats of the four substances are 1.01 J/g °C, 0.38 J/g °C, 0.45 J/g °C, and 2.00 J/g °C. What is the specific heat value of the substance that will have least increase in temperature? 0.38 J/g °C 0.45 J/g °C 1.01 J/g °C 2.00 J/g °C

Answer 1

Answer:

2.00 J/g.°C

Explanation:

To solve this problem, we can use the relation:

Q = mcΔT,

Where, Q is the amount of heat needed to raise the temperature of the substance (J).

m is the mass of the substance (g).

c is the specific heat capacity of the substance (J/g.°C).

ΔT is the temperature difference (ΔT = final T - initial T).

As clear from the relation; ΔT = Q / mc,

∵ ΔT ∝ 1/c,

The temperature difference is inversely proportional to the specific heat of the substance.

∴ The substance that will have least increase in temperature will be that has the highest specific heat capacity (2.00 J/g.°C).

Answer 2

Answer:

The substance with least increase in temperature will have highest value of specific heat and that is  2.00 J/g °C.

Explanation:

$Q=m\times c\Delta T$

Q = heat released or absorbed

m = mass of the substance

c = Specific heat of the substance

ΔT = change in temperature

$c=\frac{Q}{m\Delta T}$

The specific heats of the four substances are 1.01 J/g °C, 0.38 J/g °C, 0.45 J/g °C, and 2.00 J/g °C.

As we can see that from the above equation , specific heat of the substance is inversely linked to change in temperature.

$c\propto \frac{1}{\Delta T}$

If all the substance absorbed Q amount of heat energy:

• The substance with lower values specific heat value will have highest increase in temperature when absorbed equal amount of energy absorbed by all other substance.
• The substance with higher values specific heat value will have least increase in temperature when absorbed equal amount of energy absorbed by all other substance.

So, the substance with least increase in temperature will have highest value of specific heat and that is  2.00 J/g °C.