Assume it takes 108 joules of energy to raise the temperature of a bar of gold from 25.0°C to 29.7°C. Given that the specific heat capacity of gold is 0.128 J/g °C, what is the mass (in grams) of the bar of gold? 5.6 x 10-3 g 65 g 129 g 1.8 x 102 g none of the above
Question
Assume it takes 108 joules of energy to raise the temperature of a bar of gold from 25.0°C to 29.7°C. Given that the specific heat capacity of gold is 0.128 J/g °C, what is the mass (in grams) of the bar of gold? 5.6 x 10-3 g 65 g 129 g 1.8 x 102 g none of the above
Solution
To solve this problem, we need to use the formula for heat transfer:
Q = mcΔT
where: Q = heat energy (in joules) m = mass (in grams) c = specific heat capacity (in J/g °C) ΔT = change in temperature (in °C)
We know that Q = 108 J, c = 0.128 J/g °C, and ΔT = 29.7°C - 25.0°C = 4.7°C. We need to find m.
Rearranging the formula to solve for m gives us:
m = Q / (cΔT)
Substituting the known values gives us:
m = 108 J / (0.128 J/g °C * 4.7°C)
Calculating this gives us:
m ≈ 183.05 g
So, the mass of the bar of gold is approximately 183.05 grams. The closest answer choice to this is 1.8 x 10^2 g, so that is the correct answer.
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