It takes 45.0 J to raise the temperature of an 8.10 g piece of unknown metal from 13.0∘C to 24.3 ∘C. What is the specific heat for the metal?

0.492 J/g °C

General Formulas and Concepts:

Thermodynamics

Specific Heat Formula: q = mcΔT

q is heat (in J0m is mass (in g)c is specific heat (in J/g °C)ΔT is change in temperature (in °C)

Explanation:

Step 1: Define

Identify variables

[Given] q = 45.0 J

[Given] m = 8.10 g

[Given] ΔT = 24.3 °C - 13.0 °C = 11.3 °C

[Solve] c

Step 2: Solve for c

Substitute in variables [Specific Heat Formula]:                                             45.0 J = (8.10 g)c(11.3 °C)Multiply:                                                                                                             45.0 J = (91.53 g °C)cIsolate c:                                                                                                            0.491642 J/g °C = cRewrite:                                                                                                             c = 0.491642 J/g °C

Step 3: Check

Follow sig fig rules and round. We are given 3 sig figs.

0.491642 J/g °C ≈ 0.492 J/g °C