3/2/2016 An unknown substance at a temperature of 20 degrees Celsius is warmed up to 50 degrees when water at 80 degrees is added to it. The sum of the masses of the unknown substance and water is equal to 1000grams. In another experiment, the same substance at 20 degrees is warmed up to 52 degrees when the mass of the substance is 70 grams less than the original mass and water (same mass) at 80 degrees is added to it (masses add up to 930 grams). Find the specific heat of the unknown substance.
let u be the mass of the unknown substance of specific heat H.
uH(50-20)+(1000-u)cwater*(50-80)=0
after that, third sentence, makes no sense to me.
To find the specific heat of the unknown substance, we need to use the formula:
Q = mcΔT
Where:
Q is the heat absorbed or released by the substance,
m is the mass of the substance,
c is the specific heat of the substance, and
ΔT is the change in temperature.
Let's analyze the first experiment:
1. Unknown substance at 20 degrees Celsius is warmed up to 50 degrees when water at 80 degrees is added to it. The sum of the masses of the unknown substance and water is equal to 1000 grams.
Let the mass of the unknown substance be x grams.
The mass of water added is (1000 - x) grams.
The heat gained by the unknown substance (Q_substance) can be calculated as follows:
Q_substance = mxΔT_substance
Where:
ΔT_substance = Final temperature - Initial temperature = (50 - 20) = 30 degrees Celsius
The heat gained by the water (Q_water) can be calculated as follows:
Q_water = (1000 - x) * C_water * ΔT_water
Where:
C_water is the specific heat of water (assumed to be 1 cal/g°C) and
ΔT_water = Final temperature (50) - Initial temperature (80) = -30 degrees Celsius. (Negative because the water loses heat.)
Since the total heat lost by the water is equal to the total heat gained by the substance (according to the law of conservation of energy), we can set up the equation:
Q_substance = Q_water
mxΔT_substance = (1000 - x) * C_water * ΔT_water
Substituting the values we know:
x * 30 = (1000 - x) * 1 * -30
30x = (-30000 + 30x)
30x - 30x = -30000
0 = -30000
This equation has no solution, which means there is an error in the provided information or assumptions. Please double-check the given data and calculations to proceed with finding the specific heat of the unknown substance.