A 599 g piece of silver at 150 degrees C is submerged in 1000 g of water at 5 degrees C to be cooled. Determine the final temperature of he silver and water given
Heat capacity of water= 4.18 x 10^3 j/kg degrees C
Heat capacity of silver= 2.49 x 10^2 j/kg degrees C
The sum of the heats gained is zero.
heatgainedbywater+heatgainedbysilver=0
1000*cw(Tf-5)+599(cs)(Tf-150)=0
solve for Tf
To determine the final temperature of the silver and water, we can use the principle of conservation of energy. The energy lost by the silver equals the energy gained by the water.
Let's break down the steps to calculate the final temperature:
Step 1: Calculate the energy lost by the silver.
The energy lost by the silver can be calculated using the formula:
Energy = mass * heat capacity * change in temperature
Given:
Mass of silver = 599 g = 0.599 kg
Heat capacity of silver = 2.49 x 10^2 J/kg degrees C
Initial temperature of silver = 150 degrees C
Final temperature of silver = unknown
Using the formula for energy and rearranging for the final temperature, we have:
Energy lost by silver = Mass of silver * Heat capacity of silver * (Final temperature of silver - Initial temperature of silver)
Step 2: Calculate the energy gained by the water.
The energy gained by the water can be calculated using the same formula as above:
Energy gained by water = Mass of water * Heat capacity of water * (Final temperature of water - Initial temperature of water)
Given:
Mass of water = 1000 g = 1 kg
Heat capacity of water = 4.18 x 10^3 J/kg degrees C
Initial temperature of water = 5 degrees C
Final temperature of water = unknown
Step 3: Set up the equation and solve for the final temperature.
Since energy lost by silver = energy gained by water, we can set up the equation:
(Mass of silver * Heat capacity of silver * (Final temperature of silver - Initial temperature of silver)) = (Mass of water * Heat capacity of water * (Final temperature of water - Initial temperature of water))
Now we can plug in the values and solve for the final temperature of both the silver and water.
0.599 * 2.49 x 10^2 * (Final temperature of silver - 150) = 1 * 4.18 x 10^3 * (Final temperature of water - 5)
Now rearrange the equation and solve for the final temperature:
(0.599 * 2.49 x 10^2) * (Final temperature of silver - 150) = (1 * 4.18 x 10^3) * (Final temperature of water - 5)
Remove the parentheses:
(0.599 * 2.49 x 10^2 * Final temperature of silver) - (0.599 * 2.49 x 10^2 * 150) = (1 * 4.18 x 10^3 * Final temperature of water) - (1 * 4.18 x 10^3 * 5)
Now, rearrange the equation to solve for Final temperature of silver and Final temperature of water separately:
(0.599 * 2.49 x 10^2 * Final temperature of silver) = (1 * 4.18 x 10^3 * Final temperature of water) - (1 * 4.18 x 10^3 * 5) + (0.599 * 2.49 x 10^2 * 150)
Final temperature of silver = ((1 * 4.18 x 10^3 * Final temperature of water) - (1 * 4.18 x 10^3 * 5) + (0.599 * 2.49 x 10^2 * 150)) / (0.599 * 2.49 x 10^2)
Now you can plug in the values and calculate the final temperature of the silver. Substitute this value back into the equation to calculate the final temperature of the water.