90.0 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 21.3, what is the mass of the steel bar?
Specific heat of water = 4.18
Specific heat of steel = 0.452
The sume of the heats gained is zero (some heats gained are negative). Because I cannot read the units above,
masswater*cw*(21.3-22)+masssteel*csteel*(21.3-2)=0
solve for mass steel
To solve this problem, we can use the principle of conservation of energy, also known as heat transfer.
The heat lost by the steel rod will be equal to the heat gained by the water.
The heat lost by the steel rod can be calculated using the formula:
Q_lost = (mass of steel) * (specific heat of steel) * (final temperature - initial temperature)
The heat gained by the water can be calculated using the formula:
Q_gained = (mass of water) * (specific heat of water) * (final temperature - initial temperature)
Since the steel rod is at a lower initial temperature than the water, it will lose heat to the water. Therefore, the heat lost by the steel rod will be equal to the heat gained by the water. We can set up the equation:
(mass of steel) * (specific heat of steel) * (final temperature - initial temperature of steel) = (mass of water) * (specific heat of water) * (final temperature - initial temperature of water)
Let's substitute the given values into the equation:
(mass of steel) * (0.452) * (21.3 - 2.0) = (90.0) * (4.18) * (21.3 - 22.0)
Simplifying the equation further:
(mass of steel) * (19.3) * (0.452) = (90.0) * (4.18) * (-0.7)
Dividing both sides of the equation by (19.3 * 0.452):
mass of steel = (90.0) * (4.18) * (-0.7) / (19.3 * 0.452)
Now, calculate the mass of the steel bar using a calculator:
mass of steel = -6.156 kg
Since mass cannot be negative, the mass of the steel bar is approximately 6.16 kg.