In a laboratory experiment, a calorimeter is used to find the specific heat of an unknown metal. 100.0 grams of dry metal shot are placed in a cup and heated to a temperature of 95 °C. The calorimeter is partially filled with 150 g of water at 20.0 °C. The mass of the inner aluminum cup and of the aluminum stirrer is 60.0 g. The hot shot is poured quickly into the cup and the calorimeter is sealed. After the system has reached thermal equilibrium, the final temperature is 24.0 °C. What is the specific heat of the metal?

Question

In a laboratory experiment, a calorimeter is used to find the specific heat of an unknown metal. 100.0 grams of dry metal shot are placed in a cup and heated to a temperature of 95 °C. The calorimeter is partially filled with 150 g of water at 20.0 °C. The mass of the inner aluminum cup and of the aluminum stirrer is 60.0 g. The hot shot is poured quickly into the cup and the calorimeter is sealed. After the system has reached thermal equilibrium, the final temperature is 24.0 °C. What is the specific heat of the metal?

Answer 1

To find the specific heat of the metal, you can use the equation:

Q = mcΔT

Where:
Q is the heat energy transferred
m is the mass of the substance
c is the specific heat capacity
ΔT is the change in temperature

In this case, the heat energy transferred, Q, is equal to the heat gained or lost by the metal (Hm), the heat gained or lost by the water (Hw), and the heat lost by the cup and stirrer (Hc):

Q = Hm + Hw + Hc

Hm is the heat gained or lost by the metal, which can be calculated using the equation:

Hm = mcΔTm

Hw is the heat gained or lost by the water, which can be calculated using the equation:

Hw = mwCwΔTw

Hc is the heat lost by the cup and stirrer, which can be calculated using the equation:

Hc = mcupCcupΔTcup + mstirrerCstirrerΔTstirrer

In these equations:
m is the mass of the substance (metal, water, cup, stirrer)
c is the specific heat capacity
ΔT is the change in temperature (final temperature - initial temperature)

Now, let's calculate each term:

1. Hm:
m = mass of metal = 100.0 g
c = specific heat of the metal (unknown)
ΔTm = final temperature of the metal - initial temperature of the metal
= 24.0 °C - 95 °C

2. Hw:
mw = mass of water = 150 g
Cw = specific heat capacity of water = 4.18 J/g°C (given)
ΔTw = final temperature of the water - initial temperature of the water
= 24.0 °C - 20.0 °C

3. Hc:
mcup = mass of cup = 60.0 g
Ccup = specific heat capacity of the cup (usually given, but not provided in the question)
ΔTcup = final temperature of the cup - initial temperature of the cup
= 24.0 °C - 20.0 °C

mstirrer = mass of stirrer = 60.0 g
Cstirrer = specific heat capacity of the stirrer (usually given, but not provided in the question)
ΔTstirrer = final temperature of the stirrer - initial temperature of the stirrer
= 24.0 °C - 20.0 °C

Now that you have all the information necessary, you can substitute the values into the equations and solve for the specific heat of the metal (c).