Question

A 52 gram sample of an unknown metal requires 714 Joules of energy to heat it from

30.5◦C to 82◦C. What is the specific heat of
this metal?
Answer in units of J/g ·
◦ C.

Answer 1

Answer: Approximately
`0.267 \frac{\text{J}}{\text{g}^(\circ)\text{C}}`

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Work Shown:

We have the following variables

• Q = 714 joules = heat required
• m = 52 grams = mass
• c = specific heat = unknown
• 
  `\Delta t` = 82-30.5 = 51.5 = change in temperature

note: the symbol
`\Delta` is the uppercase Greek letter delta. It represents the difference or change in a value.

Apply those values into the formula below. Solve for c.

`Q = m*c*\Delta t\\\\714 = 52*c*51.5\\\\714 = 52*51.5*c\\\\714 = 2678*c\\\\2678*c = 714\\\\c = (714)/(2678)\\\\c \approx 0.26661687826737\\\\c \approx 0.267\\\\`

The specific heat of the unknown metal is roughly
`0.267 \frac{\text{J}}{\text{g}^(\circ)\text{C}}`