Question

If a 20.0 g object at a temperature of 35.0∘C has a specific heat of 2.89Jg∘C, and it releases 450. J into the atmosphere, what will be the final temperature of the object? Report your answer with the correct number of significant figures.

Answer 1

Answer:

The final temperature of the object will be 42.785 °C

Explanation:

When the heat added or removed from a substance causes a change in temperature in it, this heat is called sensible heat.

In other words, sensible heat is the amount of heat that a body absorbs or releases without any changes in its physical state (phase change), so that the temperature varies.

The equation for calculating the heat exchanges in this case is:

Q = c * m * ΔT

where Q is the heat exchanged by a body of mass m, constituted by a substance of specific heat c and where ΔT is the variation in temperature.

In this case:

• Q= 450 J
• c= 2.89 $\frac{J}{g*C}$
• m= 20 g
• ΔT= Tfinal - Tinitial= Tfinal - 35 °C

Replacing:

450 J= 2.89 $\frac{J}{g*C}$ *20 g* (Tfinal - 35°C)

Solving for Tfinal:

$\frac{450 J}{2.89\frac{J}{g*C}*20g} =Tfinal -35C$

7.785 °C=Tfinal - 35°C

7.785 °C + 35°C= Tfinal

42.785 °C=Tfinal

The final temperature of the object will be 42.785 °C

Answer 2

Answer: 27.2 degrees C

Explanation:

The final temperature can be determined by rearranging the specific heat capacity equation for ΔT and substituting the known values of mass, specific heat, and the heat released (which is represented by a negative number).

qcm=ΔT

−450 J / (2.89 Jg∘C)(20.0 g) = ΔT

-7.79∘C=ΔT

The negative sign of ΔT makes sense, as we know that energy is released in this exothermic process:

(Tinitial+ΔT=Tfinal)

35.0∘C+(–7.79∘C) = 27.2∘C