Question

the specific heat capacity for aluminum is 0.89 J/g °C. How much energy (in joules) is required to heat 12 grams of aluminum from 21°C to 52°C?​

Answer 1

Approximately
`330\; {\rm J}` (
`3.30 * 10^(2)\; {\rm J}`, rounded to
`2` significant figures.)

Step-by-step explanation:

Consider a material with a specific heat capacity of
`c`. Increasing the temperature of
`m` (mass) of this material by
`\Delta T` would require
`Q = c\, m\, \Delta T` of energy.

In this question:

• The specific heat capacity of aluminum is:
  `c = 0.89\; {\rm J \cdot g^(-1) \cdot (^(\circ) C)^(-1)}`.
• The mass of the aluminum to heat up is:
  `m = 12\; {\rm g}`.

The question asked for a temperature increase of
`\Delta T = (52 - 21) \; {\rm ^(\circ) C} = 31\; {\rm ^(\circ) C}`. Apply the equation
`Q = c\, m\, \Delta T` to find the amount of energy
`Q` required for this temperature change:

`\begin{aligned} Q &= c\, m\, \Delta T \\ &= 0.89\; {\rm J \cdot g^(-1) \cdot (^(\circ) C)^(-1)} * 12\; {\rm g} * 31 \; {\rm {^(\circ) C} \\ &\approx 3.3 * 10^(2)\; {\rm J}\end{aligned}`.