85.0 of is initially at room temperature (22.0). A chilled steel rod at 2.0 is placed in the water. If the final temperature of the system is 21.2, what is the mass of the steel bar? Specific heat of water = 4.18 Specific heat of steel = 0.452
My answer was 32.752. I rounded it to 32.75 and it is wrong so i rounded to 32.7, then to 32.8 all in gram and Im still wrong. Please i need help. I don't know what i am doing wrong. Thanks for your help
To solve this problem, you can use the principle of heat transfer. The formula for heat transfer is:
Q = m * c * ∆T
Where:
Q is the heat transferred
m is the mass of the substance
c is the specific heat of the substance
∆T is the change in temperature
For this problem, we have two substances, water and steel, and they both reach a final temperature of 21.2°C.
First, let's calculate the heat transferred between the water and the steel rod.
Qwater = mwater * cwater * ∆Twater
Qsteel = msteel * csteel * ∆Tsteel
The heat transferred from the hot water to the steel rod is equal to the heat transferred from the steel rod to the cold water, so:
Qwater = -Qsteel (negative sign because one gains heat while the other loses it)
We can rearrange the equation and solve for msteel:
msteel = (Qwater) / (csteel * ∆Tsteel)
Now, let's substitute the known values into the equation:
Qwater = mwater * cwater * ∆Twater (Equation 1)
Qwater = -Qsteel = -msteel * csteel * ∆Tsteel (Equation 2)
Substitute Equation 1 into Equation 2:
mw * cw * ∆Tw = -msteel * csteel * ∆Tsteel
Rearrange the equation to solve for msteel:
msteel = (-mw * cw * ∆Tw) / (csteel * ∆Tsteel)
Now, plug in the given values:
mw = 85.0 g
cw = 4.18 (specific heat of water)
∆Tw = 21.2 - 22.0 = -0.8°C (change in water temperature)
csteel = 0.452 (specific heat of steel)
∆Tsteel = 21.2 - 2.0 = 19.2°C (change in steel temperature)
msteel = (-85.0 g * 4.18 * -0.8°C) / (0.452 * 19.2°C)
Calculate the result:
msteel = 32.6517 g (rounded to four decimal places)
Therefore, the mass of the steel bar is approximately 32.65 grams, not 32.75 grams as you initially calculated.
It's worth noting that rounding errors can accumulate, so it's best to use the full calculated value for precise calculations. But if you must round, it's generally recommended to only round the final answer, rather than intermediate steps, to minimize rounding errors.