 ## July 19, 2012

### Latent Heat & Specific Heat Energy: Numerical Problems

Thermodynamics is the science of thermal energy of matter. It is study of laws that governs the conversion of energy from one form to another.

Energy is the capacity to do work or energy is that ability which causes change.

Law of conversion of energy: Energy cannot be created nor be destroyed. Energy only transform from one from to another.

Heat is a form of energy and this energy will only transfer between two or more than two systems or bodies. Heat energy always transfers from higher potential to lower potential.

Kinds of Energy:
There are several types of energies some of them are listed below
• Thermal Energy
• Mechanical Energy
• Kinetic Energy
• Potential Energy
• Electrical Energy
• Magnetic Energy
• Chemical Energy
• Nuclear Energy
As we are dealing with heat energy so we will only discuss heat energy. Some important points regarding heat:
• Heat is the only source which changes the internal energy of a body.
• We only observe or feel the heat by thermal contact.
• When heat flows from higher potential to lower potential it always raise the temperature.
• As heat always transfers from body with higher potential towards the body with lower potential. If we want to flow heath from lower potential to higher potential we have to done work against the nature.
• Both bodies should be in thermal equilibrium.
• There must be a temperature difference between the two bodies.
• The transferring energy is called heat energy and after transfer it becomes internal energy of that system.
Definitions:
• Temperature is the measure of internal energy of a body.
• Specific Heat is the amount of energy required to raise the 1°C temperature of a body of unit mass. (Mathematical formula Q = mCΔT)
• Latent Heat is that energy which is required by a body or substance when it changes is state, that is it goes from either solid to liquid or from liquid to gas. (Mathematical formula Q = mL)
Heath Energy Formulas:
1. Specific Heat: Q = mCΔT
2. Latent Heat: Q = mL
Where:
• Q = Amount of Heat
• m = Mass of body
• C = Specific Heat (Constant Value)
• L = Latent Heat (Constant Value)
• ΔT = Change in Temperature (Delta T = Final Temperature - Initial Temperature)
Numerical Problem # 1: How many Joule and BTU of heat energy is required to change 4.5 Kg of of ice at -15°C to steam at 121°C ?

Numerical Problem # 2: A rapidly spinning pedal wheel raises the temperature of 20 ml of water from 21°C to 25°C. Calculate the work done in the thermodynamic process. Calculate the heat transferred.

Numerical Problem # 3: An ice cube having mass of 50 grams and initial temperature of -10°C is dropped in 400 gram of water at 40°C (temp. of water). What is the final state, mass and temperature of the mixture if the effects of the container can be neglected ?

Some constant / values we should know before solving the problems:
• Specific heat of Ice, C(ice) = 2060 J/KgK
• Specific heat of Water, C(water) = 4186 J/KgK
• Specific heat of Steam, C(steam) = 1870 J/KgK
• Latent heat of Ice Fusion (Melting), L(fusion) = 334 KJ/Kg
• Latent heat of Ice Vaporization (Steam), L(steam) = 2260 KJ/Kg
Click on link for solution to these problems (Heat Energy Numerical Problems for EM&T Students) 