Question

Determine the final temperature of a gold nugget (mass = 376 g) that starts at 288 K and loses 4.85 kJ of heat to a snowbank when it is lost. The specific heat capacity of gold is 0.128 J/g°C.

Options:
a. 389 K
b. 133 K
c. 288 K
d. 377 K

Answer 1

To find the final temperature of a 376 g gold nugget losing 4.85 kJ of heat, the specific heat formula is used, resulting in a final temperature around 116 K. The provided options do not match this result, suggesting an error in the question or options.

The correct answer is none of all.

Step-by-step explanation:

To determine the final temperature of the gold nugget, we can use the formula that relates the change in heat (ΔQ), mass (m), specific heat capacity (c), and change in temperature (ΔT): ΔQ = m × c × ΔT. Since the gold nugget loses heat, ΔQ will be negative. Rearranging the formula to solve for the final temperature (Tfinal), we have Tfinal = Tinitial + (ΔQ / (m × c)). We are given: m = 376 g, c = 0.128 J/g°C, Tinitial = 288 K, and ΔQ = -4.85 kJ (or -4850 J since 1 kJ = 1000 J).

Substituting the values we have: Tfinal = 288 K + (-4850 J / (376 g × 0.128 J/g°C)). First, calculate the denominator: 376 g × 0.128 J/g°C = 48.128 J/°C. Then divide -4850 J by 48.128 J/°C = -100.76°C. Since the temperature change is negative, the final temperature will be lower: Tfinal = 288 K - 100.76°C. To convert from Celsius to Kelvin, add 273.15 to the Celsius change: -100.76°C + 273.15 = 172.39 K. Now subtract this from the initial temperature in Kelvin: Tfinal = 288 K - 172.39 K = 115.61 K, which rounds to 116 K. This does not match any of the options, which likely indicates a typo or error in the question or options. The correct final temperature should be close to 116 K.