A 0.190 kg piece of copper is heated and fashioned into a bracelet. The amount of energy transferred by heat to the copper is 6.62 × 104 J. If the specific heat of copper is 385 J/kg • K what is the change in the temperature of the copper?

1 answer

To find the change in temperature of the copper, we can use the formula for heat transfer:

\[ Q = mc\Delta T \]

where:

  • \( Q \) is the heat energy transferred (in joules),
  • \( m \) is the mass of the copper (in kg),
  • \( c \) is the specific heat capacity of copper (in J/kg·K),
  • \( \Delta T \) is the change in temperature (in K or °C).

Given:

  • \( Q = 6.62 \times 10^4 \) J,
  • \( m = 0.190 \) kg,
  • \( c = 385 \) J/kg·K.

We need to rearrange the formula to solve for \( \Delta T \):

\[ \Delta T = \frac{Q}{mc} \]

Now, substituting in the values:

\[ \Delta T = \frac{6.62 \times 10^4 , \text{J}}{0.190 , \text{kg} \times 385 , \text{J/kg·K}} \]

Calculating the denominator:

\[ 0.190 , \text{kg} \times 385 , \text{J/kg·K} = 73.15 , \text{J/K} \]

Now we can substitute back into the equation:

\[ \Delta T = \frac{6.62 \times 10^4 , \text{J}}{73.15 , \text{J/K}} \approx 905.53 , \text{K} \]

Thus, the change in temperature of the copper is approximately:

\[ \Delta T \approx 905.53 , \text{K} \]

So the change in temperature of the copper is about 905.53 K (or °C, since the increment of temperature in Kelvin and Celsius are the same).