An insulated beaker contains 250.0 grams of water at 25oC. Exactly 41.6 g of a
metal at 100.0oC was dropped in the beaker. The final temperature of the water
was 26.4oC. Assuming that no heat is lost in any other way, calculate the specific heat of the metal.
a. 0.159 J g-1 K-1
b. 0.478 J g-1 K-1
c. 0.0503 J g-1 K-1
d. 2.09 J g-1 K-1
i have no idea how to do this?
and yes i saw the other post but it did not help a bit
What do you mean it didn't help? Then you didn't read it (or try it). Specific heat of the metal is the ONLY unknown in that equation and if you solve for it you get one of the answers listed. I just solved it so I know that's true.
Show your work and I'll be able to tell you what you're missing.
[41.6xmx1.5]+[18x4.186x1.5]=0
6.24m+113.022=0
62.4m=-113.022
m=113.022/62.4
m=1.81125
not an answer choice?
To solve this problem, you need to use the principle of heat transfer, specifically the equation:
q = mcΔT
where q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the heat lost by the metal is equal to the heat gained by the water:
q_lost_by_metal = q_gained_by_water
To find the heat lost by the metal, you can use the equation:
q_lost_by_metal = mcΔT
Substituting the given values:
m = 41.6 g (mass of the metal)
c = ? (specific heat capacity of the metal)
ΔT = (26.4°C - 100.0°C) = -73.6°C (change in temperature)
So, the equation becomes:
q_lost_by_metal = 41.6g * c * -73.6°C
To find the heat gained by the water, you can use the equation:
q_gained_by_water = mcΔT
Substituting the given values:
m = 250.0 g (mass of the water)
c = 4.18 J/g°C (specific heat capacity of water, which is known)
ΔT = (26.4°C - 25.0°C) = 1.4°C (change in temperature)
So, the equation becomes:
q_gained_by_water = 250.0g * 4.18 J/g°C * 1.4°C
Since q_lost_by_metal = q_gained_by_water, you can set the two equations equal to each other and solve for the specific heat capacity of the metal (c):
41.6g * c * -73.6°C = 250.0g * 4.18 J/g°C * 1.4°C
Simplifying the equation:
-41.6g * c = 1,465J/g
Dividing both sides of the equation by -41.6g:
c = 1,465J/g / -41.6g
c = -35.21 J/g°C
The specific heat capacity cannot be negative, so we need to take the positive value:
c = 35.21 J/g°C
The closest option to this answer is (d) 2.09 J g-1 K-1.
Therefore, the specific heat of the metal is approximately 2.09 J g-1 K-1.