A silver block, initially at 55.1∘C, is submerged into 100.0 g of water at 25.2∘C in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 27.9∘C. The specific heat capacities for water and silver are Cs,water=4.18J/(g⋅∘C) and Cs,silver=0.235J/(g⋅∘C).
Part A
What is the mass of the silver block?
Express your answer to two significant figures and include the appropriate units.
(55.1 - 27.9) * 0.235 * m = (27.9 - 25.2) * 4.18 * 100.0
m is in grams
Why did the silver block go to the party?
Because it wanted to raise the temperature and have a melting good time!
To calculate the mass of the silver block, we can use the equation:
q_water + q_silver = 0
where q_water is the heat gained by the water and q_silver is the heat lost by the silver block.
The heat gained by the water can be calculated using the equation:
q_water = m_water * Cs,water * ΔT
where m_water is the mass of the water, Cs,water is the specific heat capacity of water, and ΔT is the change in temperature.
The heat lost by the silver block can be calculated using the equation:
q_silver = m_silver * Cs,silver * ΔT
where m_silver is the mass of the silver block, Cs,silver is the specific heat capacity of silver, and ΔT is the change in temperature.
Since the total heat gained by the water is equal to the total heat lost by the silver block, we can set up the following equation:
m_water * Cs,water * ΔT_water = m_silver * Cs,silver * ΔT_silver
Plugging in the given values:
(100.0 g) * (4.18 J/(g⋅∘C)) * (27.9∘C - 25.2∘C) = m_silver * (0.235 J/(g⋅∘C)) * (55.1∘C - 27.9∘C)
Now we can solve for m_silver. Let me calculate it for you...
Calculating...calculating...
And the mass of the silver block is approximately 28 g.
So, the mass of the silver block is 28 g.
To find the mass of the silver block, we can use the equation for heat transfer:
q = m1 * c1 * ΔT
Where:
q = heat transferred (0, as the system is insulated and no heat is gained or lost)
m1 = mass of the silver block (what we're trying to find)
c1 = specific heat capacity of silver (0.235 J/(g⋅∘C))
ΔT = change in temperature (final temperature - initial temperature)
Substituting the given values:
0 = m1 * 0.235 J/(g⋅∘C) * (27.9∘C - 55.1∘C)
Now we can solve for the mass (m1):
0 = -27.2∘C * 0.235J/(g⋅∘C) * m1
m1 = 0g (since the multiplication is 0, no mass is required)
Therefore, the mass of the silver block is 0 g.
To find the mass of the silver block, we can use the principle of conservation of energy. The heat lost by the silver block will be equal to the heat gained by the water.
We can use the following formula to calculate the heat gained or lost by an object:
Q = mcΔT
Where:
Q represents the heat gained or lost (in Joules)
m represents the mass of the object (in grams)
c represents the specific heat capacity of the substance (in J/(g⋅°C))
ΔT represents the change in temperature (in °C)
Let's assign the following variables:
m_silver: mass of the silver block (what we're trying to find)
m_water: mass of the water (given as 100.0 g)
ΔT_water: change in temperature of the water (final temperature - initial temperature = 27.9°C - 25.2°C)
ΔT_silver: change in temperature of the silver block (final temperature - initial temperature = 27.9°C - 55.1°C)
c_water: specific heat capacity of water (given as 4.18 J/(g⋅°C))
c_silver: specific heat capacity of silver (given as 0.235 J/(g⋅°C))
Using the principle of conservation of energy, we can set up the following equation:
m_silver * c_silver * ΔT_silver = m_water * c_water * ΔT_water
Substituting the known values:
m_silver * (0.235 J/(g⋅°C)) * (27.9°C - 55.1°C) = (100.0 g) * (4.18 J/(g⋅°C)) * (27.9°C - 25.2°C)
Simplifying the equation:
m_silver * (-27.2°C) * (0.235 J/(g⋅°C)) = (100.0 g) * (4.18 J/(g⋅°C)) * (2.7°C)
Dividing both sides of the equation by (-27.2°C * 0.235 J/(g⋅°C)):
m_silver = (100.0 g) * (4.18 J/(g⋅°C)) * (2.7°C) / (-27.2°C * 0.235 J/(g⋅°C))
m_silver = 9.95 g
Therefore, the mass of the silver block is approximately 9.95 grams.