Question

A 5.63 g sample of solid gold is heated from 21.0 ºC to 32.0 ºC. How much energy (in J and cal) is required?

Answer 1

The energy required to heat a 5.63 g sample of solid gold from 21.0 °C to 32.0 °C is approximately 8.0239 J or 1.9174 cal, using the specific heat capacity of gold (0.129 J/g°C).

Step-by-step explanation:

To calculate the energy required to heat the sample of solid gold, we can use the formula: q = mcΔT, where q is the heat energy in joules (J), m is the mass of the substance in grams (g), c is the specific heat capacity (J/g°C), and ΔT is the change in temperature in degrees Celsius (°C).

The mass m of solid gold is 5.63 g, and the specific heat capacity c of gold is given as 0.129 J/g°C. The change in temperature ΔT is (32.0 °C - 21.0 °C) = 11.0 °C.

Therefore, the energy required in joules is:
q = (5.63 g) × (0.129 J/g°C) × (11.0 °C) = 8.0239 J.

To convert joules to calories, we use the conversion factor: 1 cal = 4.184 J. Therefore,
q in calories is: q = 8.0239 J × (1 cal / 4.184 J) = 1.9174 cal.

The energy required to heat the sample of gold from 21.0 °C to 32.0 °C is approximately 8.0239 J or 1.9174 cal.

Answer 2

According to q formula:
q = M C ΔT
when q is the energy required in Joule
M is the mass per kilogram=5.63 g /1000 = 0.00563 Kg
C is the specific heat capacity of the gold J(Kg-K) = 125.6 J(Kg-K)(should be given in the specific heat capacity table)
ΔT is the change in the temperature = (32 - 21) = 11 C°
∴q = 0.00563 * 125.6 * 11 = 7.78 J = 1.86 Cal