HELP PLEASE. I have no idea how to set this up. I tried using the q=mc(change in temp) equation but its not working out.
A 59.8 g block of an unknown metal at 87.5 degrees Celsius was dropped into an insulated vesssel containing approximately 33 g of ice and 23 g of water at 0 degrees celsius. After the system had reached equilibrium it was determined that 6.29 g of the ice had melted.
I don't see a question here.
To solve this problem, we need to use the principle of conservation of energy and apply the specific heat equation. The specific heat equation is:
q = mc∆T
Where:
q is the heat gained or lost by the substance,
m is the mass of the substance,
c is the specific heat capacity of the substance,
∆T is the change in temperature of the substance.
Let's break down the problem step by step:
1. First, calculate the heat gained or lost by the ice that melted.
Given:
Mass of ice melted (m) = 6.29 g
Specific heat capacity of ice (c) = 2.09 J/g°C (this is the specific heat capacity of ice at 0°C)
Change in temperature (∆T) of the ice = 0°C - (-6.29°C) = 6.29°C
Use the specific heat equation:
q1 = mc∆T
q1 = (6.29 g)(2.09 J/g°C)(6.29°C)
q1 = 78.18 J
Therefore, the heat gained or lost by the ice (q1) is 78.18 J.
2. Next, calculate the heat gained or lost by the water that had no phase change.
Given:
Mass of water (m) = 23 g
Specific heat capacity of water (c) = 4.18 J/g°C (this is the specific heat capacity of water at 0°C)
Change in temperature (∆T) of the water = 0°C - 0°C = 0°C
Use the specific heat equation:
q2 = mc∆T
q2 = (23 g)(4.18 J/g°C)(0°C)
q2 = 0 J
Therefore, the heat gained or lost by the water (q2) is 0 J since there was no change in temperature.
3. Now, calculate the heat gained or lost by the metal.
Given:
Mass of metal (m) = 59.8 g
Initial temperature of the metal = 87.5°C
Final temperature of the metal = 0°C
Use the specific heat equation:
q3 = mc∆T
q3 = (59.8 g)(c)(0°C - 87.5°C)
q3 = (59.8 g)(c)(-87.5°C)
Unfortunately, you didn't provide the specific heat capacity (c) of the metal. The specific heat capacity varies for different metals. You will need to refer to a reliable source or the information given in your problem to determine the specific heat capacity of the metal.
Once you have the specific heat capacity of the metal, you can substitute the value into the equation and calculate q3.
4. Finally, since energy is conserved, the total heat gained or lost by the system is equal to zero.
q1 + q2 + q3 = 0
Substitute the known values and solve for q3.
Remember to use the correct signs for heat gained or lost (+/-) depending on the direction of heat flow.
I hope this explanation helps you solve the problem!