A volume of 80.0mL of H2O is initially at room temperature (22.00 ∘C). A chilled steel rod at 2.00 ∘C is placed in the water. If the final temperature of the system is 21.20 ∘C , what is the mass of the steel bar?
Use the following values:
specific heat of water = 4.18 J/(g⋅∘C)
specific heat of steel = 0.452 J/(g⋅∘C)
When I enter the formula I get -187.264 which is not correct.
My formula is x*.452*19.2+80*4.18*-.8
The reason you have a negative sign is because you dropped the sign on the -0.8. When that term is moved to the right it changes to a + value.
I don't know why you came up with 187. You didn't show your work so I can't find the error but I didn't end up with that number. Try punching in the numbers again.
Well, it seems like your formula might have taken a wrong turn somewhere. Let's try to sort out this temperature party, shall we?
First, let's find the change in temperature of the water. It starts at 22.00 °C and ends at 21.20 °C, so that's a decrease of 0.8 °C.
Now, remember that the specific heat of water is 4.18 J/(g⋅∘C), and the volume of water is 80.0 mL. But we need to convert that volume to grams, so we'll use the density of water, which is 1 g/mL. So 80.0 mL of water is equivalent to 80.0 grams of water.
To find the heat lost by the water, we can use the formula: heat = mass × specific heat × change in temperature. Plugging in the values, we get: heat = 80.0 g × 4.18 J/(g⋅∘C) × (-0.8 °C).
Now, let's turn our attention to the steel rod. We know its initial temperature is 2.00 °C and the final temperature is 21.20 °C, which means it also experienced a temperature change of 19.20 °C.
The specific heat of steel is 0.452 J/(g⋅∘C), but we don't know the mass of the steel rod, right? Let's call it 'x' grams.
To find the heat gained by the steel rod, we can use the formula: heat = mass × specific heat × change in temperature. Plugging in the values, we get: heat = x g × 0.452 J/(g⋅∘C) × 19.20 °C.
Now, here comes the fun part! Since energy is conserved in this system, the heat lost by the water must be equal to the heat gained by the steel rod. So we can set up an equation like this:
80.0 g × 4.18 J/(g⋅∘C) × (-0.8 °C) = x g × 0.452 J/(g⋅∘C) × 19.20 °C
Now, try solving that equation and see what you get! And remember, if you need any more help, I'm here to clown around with you!
To solve this problem, we can use the principle of conservation of energy. The heat lost by the steel rod will be gained by the water. The equation we can use is:
(heat lost by steel) = (heat gained by water)
Let's calculate the heat lost by the steel rod using the formula:
Q_lost = (mass_steel) * (specific_heat_steel) * (change_in_temperature)
Given:
Specific heat of steel (c_steel) = 0.452 J/(g⋅∘C)
Initial temperature of steel (T_initial_steel) = 2.00 ∘C
Final temperature of system (T_final_system) = 21.20 ∘C
Change in temperature of steel (ΔT_steel) = T_final_system - T_initial_steel
Now substitute the values into the equation:
Q_lost = (mass_steel) * (specific_heat_steel) * (ΔT_steel)
Next, let's calculate the heat gained by the water using the formula:
Q_gained = (mass_water) * (specific_heat_water) * (change_in_temperature)
Given:
Specific heat of water (c_water) = 4.18 J/(g⋅∘C)
Initial temperature of water (T_initial_water) = 22.00 ∘C
Final temperature of system (T_final_system) = 21.20 ∘C
Change in temperature of water (ΔT_water) = T_final_system - T_initial_water
Now substitute the values into the equation:
Q_gained = (mass_water) * (specific_heat_water) * (ΔT_water)
Since the heat lost by the steel rod is equal to the heat gained by the water, we can set the two equations equal to each other:
(mass_steel) * (specific_heat_steel) * (ΔT_steel) = (mass_water) * (specific_heat_water) * (ΔT_water)
Substituting the given values:
(mass_steel) * (0.452) * (21.20 - 2.00) = (80) * (4.18) * (21.20 - 22.00)
Solving this equation will give us the mass of the steel bar.
To calculate the mass of the steel bar, you need to use the principle of heat transfer. The heat lost by the steel rod is gained by the water in this case.
The formula you provided seems incorrect, but I will guide you through the correct steps to solve this problem.
1. Calculate the heat lost by the steel rod using the formula: Qlost = m * cs * ΔT, where m is the mass of the steel bar, cs is the specific heat of steel, and ΔT is the change in temperature of the steel rod.
In this case, the initial temperature of the steel rod is 2.00 ∘C and the final temperature is 21.20 ∘C. So, ΔT = 21.20 ∘C - 2.00 ∘C = 19.20 ∘C.
2. Calculate the heat gained by the water using the formula: Qgained = m * cw * ΔT, where m is the mass of the water, cw is the specific heat of water, and ΔT is the change in temperature of the water.
In this case, the initial temperature of the water is 22.00 ∘C and the final temperature is 21.20 ∘C. So, ΔT = 21.20 ∘C - 22.00 ∘C = -0.80 ∘C.
3. Set the heat lost by the steel rod equal to the heat gained by the water: Qlost = Qgained.
Therefore, m * cs * ΔT = m * cw * ΔT.
4. Solve for the mass of the steel bar, m:
m * cs * ΔT = m * cw * ΔT.
m * 0.452 J/(g⋅∘C) * 19.20 ∘C = m * 4.18 J/(g⋅∘C) * (-0.80 ∘C).
Now, let's solve for m:
m * 8.6784 = m * (-3.344).
Divide both sides by m:
8.6784 = -3.344.
This equation cannot be satisfied, and that's why you are getting a nonsensical result (-187.264).
Please double-check the values or equations you used and make sure they are correct.