Final answer:
To find the specific heat of brass, the heat gained by 335 g of water when its temperature increased from 25.0°C to 32.0°C was calculated and found to be 9817 J. This heat gain equals the heat loss by 410 g of brass as it cools from 95.0°C to 32.0°C. The specific heat of the brass was determined to be approximately 0.381 J/g°C.
Step-by-step explanation:
To determine the specific heat of brass using the thermal energy gained by water, we start by calculating the heat absorbed by the water as it is heated from 25.0℃ to 32.0℃. Assuming no heat loss to the surroundings, the heat lost by the brass will equal the heat gained by the water.
The heat gained by the water can be calculated using the formula:
q = mwater × cwater × ΔTwater
where q is the heat gained, mwater is the mass of the water (335 g), cwater is the specific heat capacity of water (4.18 J/g°C), and ΔTwater is the change in temperature (32.0℃ - 25.0℃ = 7.0℃).
Heat gained by water: q = 335 g × 4.18 J/g℃ × 7.0℃ = 9817 J.
Now we can use the heat lost by brass to calculate its specific heat (cbrass), using the formula:
q = mbrass × cbrass × ΔTbrass
Since the heat lost by brass is equal to the heat gained by water, we rearrange the formula to solve for cbrass:
cbrass = q / (mbrass × ΔTbrass)
ΔTbrass is the temperature change of brass, which is (95.0℃ - 32.0℃) and mbrass is the mass of the brass (410 g).
cbrass = 9817 J / (410 g × (95.0℃ - 32.0℃))
After performing the calculations:
cbrass = 9817 J / (410 g × 63.0℃) = 0.381 J/g℃ (Approximately)
The specific heat of brass is approximately 0.381 J/g℃.