Question

A copper calorimeter can with mass 0.100kg contains 0.160kg of water and 0.018kg of ice in thermal equilibrium at atmospheric pressure.
Part A
If 0.750kg of lead at a temperature of 255 c is dropped into the calorimeter can, what is the final temperature? Assume that no heat is lost to the surroundings

Answer 1

Concepts and reason

The concept to solve this problem is the principle of calorimetry.

Firstly, find the heat lost by the lead when it is put in the calorimeter by the expression of heat.

Then, find the heat gained by the calorimeter by using the expression of heat and the latent heat.

Finally, equate both expressions to find the final temperature reached by the system in equilibrium.

Fundamentals

The heat lost by a system when its temperature changes from initial (T_i) to equilibrium temperature (T_f) can be expressed as follows:

$AQ=mC(T:-T) $

Here, m is the mass of the system and C is the specific heat capacity of the system.

The heat gained by the system due to change in temperature from initial temperature (T_i) to equilibrium temperature (T_f) can be expressed as follows:

Here, m is the mass of the system and C is the specific heat capacity of the system.

The heat required to change a solid into liquid without changing its temperature is as follows:

$Q=mL $

Here, m is the mass of the solid and is the latent heat of solid.

The lead is initially at the temperature and when dropped into the Calorimeter, it attains a final temperature at equilibrium. The heat lost by the lead is as follows:

$AQ=mC(T:-T) $

Substitute 0.750 kg for m, for C, for , and T for final equilibrium temperature in the above expression.

The heat gained by the system due to change in temperature from initial temperature (T_i) to equilibrium temperature (T_f) can be expressed as follows:

When the hot substance lead is dropped into the can, the temperature of the substances inside the can rises and the heat is gained by the substances. The substances inside the can are ice and water. The heat gained by the substances in the can () is as follows:

Here, is the total mass of the substance inside the can.

The calorimeter contains ice such that its temperature must be at 0 degrees Celsius initially.

Substitute 0.018 kg for m_ice, 0.160 kg for m_water, for C_water, T for T_i and for in the above expression.

The heat is also gained by the calorimeter by the change in the temperature of the copper can. The heat gained by the copper container is as follows:

Substitute 0.100 kg for m_c, for C_c, T for T_f and for in the above expression.

The heat gained by the ice when its phase changes from ice to water is as follows:

$Q=mL $

Substitute 0.018 kg for m_ice, 334000 J/kg for L_f in the above expression.

The net heat gained by the system is the sum of all the heat changes. The net heat gained is as follows:

Substitute 6012 J for Q, for, and for in the above expression.

The heat gained by the calorimeter is equal to the heat lost by the lead.

Equate equation with equation .

Ans:

The equilibrium temperature is.