A calorimeter contained 75g of water at 16.95 degree Celsius. A 93.3g Iron at 65.58 degrees celsius was placed in it, giving a final temperature of 19.68 degrees Celsius for the system. Calculate the heat capacity of the calorimeter. specific heats are 4.184J/gdegrees Celsius and 0.444J/gdegrees Celsius for Fe.
So the heat gained + heat lost is zero.
75*cwater*(19.68-16.95)+HeatCapictyCalorimeter*(19.68-16.95)+93.3*ciron*(19.68-65.58)=0
solve for heatcapacity of calormeter.
heat lost by the iron was gained by the water and the calorimeter
heat capacity is the same as specific heat
To calculate the heat capacity of the calorimeter, we need to consider the heat gained by the water, heat gained by the iron, and heat lost by the calorimeter. The equation to calculate the heat is Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
First, let's calculate the heat gained by the water:
Q1 = mcΔT1 = 75g * 4.184J/g°C * (19.68°C - 16.95°C)
Next, let's calculate the heat gained by the iron:
Q2 = mcΔT2 = 93.3g * 0.444J/g°C * (19.68°C - 65.58°C)
Since energy is conserved in a closed system, the heat gained by the water and the iron should be equal to the heat lost by the calorimeter. Therefore, we can set up the following equation:
Q1 + Q2 = -CΔT
where C is the heat capacity of the calorimeter and ΔT is the change in temperature for the system.
Now, let's solve for C. Rearranging the equation, we get:
- C = (Q1 + Q2) / ΔT
Plug in the values:
- C = ((75g * 4.184J/g°C * (19.68°C - 16.95°C)) + (93.3g * 0.444J/g°C * (19.68°C - 65.58°C))) / (19.68°C - 16.95°C)
After calculating the numerator and denominator, we can find the value of C:
- C = -365.64 J/°C
Since heat capacity is a positive value, we take the absolute value of -365.64 J/°C:
C (heat capacity of the calorimeter) = 365.64 J/°C
Therefore, the heat capacity of the calorimeter is 365.64 J/°C.
To calculate the heat capacity of the calorimeter, we need to use the principle of heat transfer and energy conservation.
The equation for heat transfer is:
q = m * c * ΔT
where:
- q is the heat transferred
- m is the mass
- c is the specific heat capacity
- ΔT is the change in temperature
First, let's calculate the heat transferred to the water:
q_water = m_water * c_water * ΔT_water
= 75g * 4.184 J/g°C * (19.68°C - 16.95°C)
Next, calculate the heat transferred to the iron:
q_iron = m_iron * c_iron * ΔT_iron
= 93.3g * 0.444 J/g°C * (19.68°C - 65.58°C)
Since energy is conserved in this closed system, the heat transferred to the water must be equal to the heat transferred to the iron:
q_water = -q_iron
To find the heat capacity of the calorimeter, we need to consider that the calorimeter absorbs some heat. Thus:
q_calo = -q_water
= -m_water * c_water * ΔT_water
Finally, divide the heat transferred to the calorimeter by the change in temperature to get the heat capacity:
C_calo = q_calo / ΔT_system
where:
- C_calo is the heat capacity of the calorimeter
- ΔT_system is the change in temperature observed for the entire system
Substituting the values:
C_calo = (-q_water) / (19.68°C - 16.95°C)
Plug in the calculated values to get the final answer.