In a physics lab experiment, a student immersed 205 one-cent coins (each having a mass of 3.00 g *.003kg) in boiling water. After they reached thermal equilibrium, she quickly fished them out and dropped them into 0.244 kg of water at 20.0 C in an insulated container of negligible mass.
What was the final temperature of the coins? [One-cent coins are made of a metal alloy - mostly zinc - with a specific heat capacity of 390 J/(kg*K).]
I know that:
Mass,coins=.615 kg
Mass,water=.244 kg
c=390 J/(kg*K)
Ti,water=20 C
I'm just not quite sure what equation to put them in...
Heat lost by the coins + heat gained by the water = 0
mass x specific heat x (Tf - Ti) + mass x specific heat x (Tf - Ti) = 0
Tf is final T. Ti is initial T.
Post your work if you get stuck.
how to write up a lab on specific heat capacity
To find the final temperature of the coins, you can use the principle of thermal equilibrium. This states that when two objects at different temperatures are in contact with each other and insulated from their surroundings, they will reach a common final temperature.
To solve this problem, you can use the equation:
m1c1(Tf - T1) = m2c2(T2 - Tf)
Where:
m1 = mass of the coins (0.615 kg)
c1 = specific heat capacity of the coins (390 J/(kg*K))
Tf = final temperature of the coins (what we are trying to find)
T1 = initial temperature of the coins (boiling water, let's assume 100°C)
m2 = mass of the water (0.244 kg)
c2 = specific heat capacity of water (specific heat capacity of water is approximately 4186 J/(kg*K))
T2 = initial temperature of the water (20°C)
Plugging in the values:
(0.615 kg)(390 J/(kg*K))(Tf - 100°C) = (0.244 kg)(4186 J/(kg*K))(20°C - Tf)
Now, solve the equation for Tf.
(0.615 kg)(390 J/(kg*K))(Tf - 100°C) = (0.244 kg)(4186 J/(kg*K))(20°C - Tf)
Using algebraic manipulation, we can simplify the equation.
(234.285 kg∙J/K)(Tf - 100) = (1021.204 kg∙J/K)(20 - Tf)
Now, expand and rearrange the equation:
234.285 Tf - 23428.5 = 20424.08 - 1021.204 Tf
Combine like terms:
234.285 Tf + 1021.204 Tf = 20424.08 + 23428.5
1255.49 Tf = 43852.58
Solve for Tf:
Tf = 43852.58 / 1255.49
Tf = 34.95°C
Therefore, the final temperature of the coins is approximately 34.95°C.