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.

Question

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...

Answer 1

To find the final temperature of the coins, we can use the principle of conservation of energy.

The energy gained by the coins is equal to the energy lost by the water.

The energy gained by the coins can be calculated using the equation:

Energy gained = mass of the coins * specific heat capacity of the coins * change in temperature

The energy lost by the water can be calculated using the equation:

Energy lost = mass of the water * specific heat capacity of water * change in temperature

Since the system is in thermal equilibrium, the energy gained by the coins is equal to the energy lost by the water.

Therefore, we can set up the equation:

mass of the coins * specific heat capacity of the coins * (final temperature of the coins - initial temperature of the coins) = mass of the water * specific heat capacity of water * (final temperature of the water - initial temperature of the water)

Substituting the given values, we have:

(0.615 kg) * (390 J/(kg*K)) * (final temperature of the coins - 100°C) = (0.244 kg) * (4200 J/(kg*K)) * (20°C - 100°C)

Now we can solve for the final temperature of the coins by rearranging the equation and solving for the unknown:

(final temperature of the coins - 100°C) = (0.244 kg * 4200 J/(kg*K) * (20°C - 100°C)) / (0.615 kg * 390 J/(kg*K))

(final temperature of the coins - 100°C) = -15.5455°C

(final temperature of the coins) = -15.5455°C + 100°C

(final temperature of the coins) = 84.4545°C

So, the final temperature of the coins is approximately 84.45°C.