7. A 100g mass of tungsten at 100 degrees C is placed in 200 mL of water at 20 degrees C. The mixture reaches equilibrium at 21.6 degrees C. Calculate the specific heat of tungsten.
Ok, I tried working it out but I got
q= 100g x 4.186 j/g*degrees C * (21.6 degrees C- 20.0 degrees C) which equals to 1.6.
So q= 100g * 4.186 j/g*deg C * 1.6
I got a very high number. I am stuck what do I do?
From what I am learning right now you should be using kilos, that would definitely affect your answer.
heat lost by tungsten + heat gained by water = 0
Is that hint good enough?
To calculate the specific heat of tungsten, you need to use the concept of the heat gained by the water being equal to the heat lost by the tungsten. Here's the step-by-step calculation:
1. Calculate the heat gained by water:
To find the heat gained by the water, you'll use the formula:
q_water = m_water x c_water x ΔT_water
where:
m_water = mass of water = 200 mL = 200 g
c_water = specific heat of water = 4.186 J/g°C
ΔT_water = change in temperature of water = 21.6°C - 20.0°C = 1.6°C
So, q_water = 200 g x 4.186 J/g°C x 1.6°C = 1332.16 J
2. Calculate the heat lost by tungsten:
To find the heat lost by the tungsten, you'll use the formula:
q_tungsten = m_tungsten x c_tungsten x ΔT_tungsten
where:
m_tungsten = mass of tungsten = 100 g
c_tungsten = specific heat of tungsten (to be determined)
ΔT_tungsten = change in temperature of tungsten = 21.6°C - 100°C = -78.4°C
You have the value for q_tungsten, which is 1332.16 J (from step 1).
So, 1332.16 J = 100 g x c_tungsten x (-78.4°C)
c_tungsten = 1332.16 J / (100 g x -78.4°C) = -1.6983 J/g°C
Note: The negative sign signifies that tungsten lost heat to the water.
So, the specific heat of tungsten is approximately -1.6983 J/g°C.
To calculate the specific heat of tungsten, you need to use the concept of heat transfer and the equation q = mcΔT, where q is the heat transfer, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Let's break down the problem step by step:
1. Calculate the heat transfer (q) for the water:
q_water = m_water * c_water * ΔT_water
Here, m_water is the mass of water (200 mL), c_water is the specific heat of water (4.186 J/g*°C), and ΔT_water is the change in temperature of the water (21.6°C - 20.0°C).
2. Calculate the heat transfer (q) for the tungsten:
q_tungsten = m_tungsten * c_tungsten * ΔT_tungsten
Here, m_tungsten is the mass of tungsten (100 g), c_tungsten is the specific heat of tungsten (which you want to find), and ΔT_tungsten is the change in temperature of the tungsten (21.6°C - 100.0°C).
3. Since the system reaches equilibrium, the heat transfer for the water (q_water) should be equal to the heat transfer for the tungsten (q_tungsten).
q_water = q_tungsten
Now, let's solve the equations:
From step 1:
q_water = 200g * 4.186 J/g*°C * (21.6°C - 20.0°C)
From step 2:
q_tungsten = 100g * c_tungsten * (21.6°C - 100.0°C)
Since q_water = q_tungsten, you can equate the two equations:
200g * 4.186 J/g*°C * (21.6°C - 20.0°C) = 100g * c_tungsten * (21.6°C - 100.0°C)
Now, you can solve for c_tungsten by rearranging the equation:
c_tungsten = (200g * 4.186 J/g*°C * (21.6°C - 20.0°C)) / (100g * (21.6°C - 100.0°C))
Evaluating this expression will give you the specific heat of tungsten.