Question

what change in temperature will result from adding 1000 j of heat to 100 g of gold? the specific heat capacity of gold is 0.126 j/g°c
12,600 °c
79.37 °c
1,260 °c
not enough information is given.
7.94 °c

Explanation:

Step1: Recall the heat formula

The formula for heat transfer is \( Q = mc\Delta T \), where \( Q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature. We need to solve for \( \Delta T \), so rearrange the formula to \( \Delta T=\frac{Q}{mc} \).

Step2: Identify the given values

We know that \( Q = 1000 \, \text{J} \), \( m = 100 \, \text{g} \), and \( c = 0.126 \, \text{J/g}^\circ\text{C} \).

Step3: Substitute the values into the formula

Substitute \( Q \), \( m \), and \( c \) into \( \Delta T=\frac{Q}{mc} \):
\( \Delta T=\frac{1000}{100\times0.126} \)

Step4: Calculate the result

First, calculate the denominator: \( 100\times0.126 = 12.6 \). Then, divide \( 1000 \) by \( 12.6 \): \( \Delta T=\frac{1000}{12.6}\approx79.37^\circ\text{C} \).

Answer:

79.37 \(^\circ\)C (corresponding to the option "79.37 \(^\circ\)C")