Substance Specific Heat (J kg-1 K-1)

Aluminum 900
Copper 390
Brass 380
Silver 230
Platinum 130

If 500 J of energy were added to 1 kg of each of these samples, which would experience the LEAST temperature increase?
Responses
A AluminumAluminum
B BrassBrass
C CopperCopper
D Platinum

1 answer

To determine which substance experiences the least temperature increase when 500 J of energy is added to 1 kg of each sample, we can use the formula for temperature change:

\[ \Delta T = \frac{Q}{m \cdot c} \]

Where:

  • \(\Delta T\) is the temperature increase,
  • \(Q\) is the energy added (in joules),
  • \(m\) is the mass (in kg), and
  • \(c\) is the specific heat capacity (in J kg\(^{-1}\) K\(^{-1}\)).

For each of the given substances with 1 kg mass and \(Q = 500\) J, we can calculate the temperature increase:

  1. Aluminum: \[ \Delta T = \frac{500}{1 \cdot 900} = \frac{500}{900} \approx 0.556 , \text{K} \]

  2. Copper: \[ \Delta T = \frac{500}{1 \cdot 390} = \frac{500}{390} \approx 1.282 , \text{K} \]

  3. Brass: \[ \Delta T = \frac{500}{1 \cdot 380} = \frac{500}{380} \approx 1.316 , \text{K} \]

  4. Silver: \[ \Delta T = \frac{500}{1 \cdot 230} = \frac{500}{230} \approx 2.174 , \text{K} \]

  5. Platinum: \[ \Delta T = \frac{500}{1 \cdot 130} = \frac{500}{130} \approx 3.846 , \text{K} \]

Now comparing the temperature increases:

  • Aluminum: 0.556 K
  • Copper: 1.282 K
  • Brass: 1.316 K
  • Silver: 2.174 K
  • Platinum: 3.846 K

The substance that experiences the least temperature increase when 500 J of energy is added is Aluminum.

Thus, the correct response is: A. Aluminum