Question

If I apply 0.108 kJ of energy in order to increase the temperature of a bar of gold from 30.0°C to 34.7°C, and the specific heat capacity of gold is 0.128 J/g°C, what is the mass the bar of gold in grams? A. 1.8 × 102 g B. 6.5 × 101 g C. 1.08 × 102 g D. 1.28 × 102 g E. none of these

Answer 1

Answer:

The mass of the given gold bar: m = 1.8 × 10² g

Explanation:

The Specific heat capacity (c) of a given substance is defined as the heat capacity (C) per unit mass (m) or the energy required (Q) to increase the temperature (ΔT) of the given substance per unit mass.

∴ The specific heat capacity: $c = \frac{C}{m} =\frac{Q}{m\times \Delta T}$

Given: The specific heat capacity of gold (Au) = 0.128 J/g°C

The increase in temperature: ΔT = 34.7°C - 30.0°C = 4.7°C

Heat energy: Q = 0.108 kJ = 0.108 × 1000 J = 108 J    (∵ 1 kJ = 1000J)

Mass of the given gold bar: m = ?

Therefore, the mass of the given gold bar:

$m = \frac{Q}{c\times \Delta T}$

$m = \frac{108 J}{(0.128 J/g.^{\circ }C)\times (4.7 ^{\circ }C)}$

$m = 179.5 g = 1.795\times 10^{2} g$

$\therefore m \approx 1.8 \times 10^{2} g$

Therefore, the mass of the given gold bar: m = 1.8 × 10² g