Concepts and reasonHeat:It is a form of energy exchanged between two systems and responsible for temperature difference between the systems.Work:Work is the amount of energy transferred between two systems or from a system to its surroundings.Internal energy:The total amount of kinetic and potential energy possessed by a system itself without any external influences is termed as internal energy.First Law of thermodynamics:For a closed thermodynamic system, the variation in internal energy is equivalent to the difference in the heat energy supplied to the system and the work done by the system.Ideal gas law:An ideal gas with pressure p, temperature T, volume V and mass m obeys the following relationHere, is the gas constant.The temperature of air at state 2 can be calculated by using the ideal gas relation. Then the type of energy transfer can be obtained by using the first law of thermodynamics.
FundamentalsThe relation for the first law of thermodynamics is as follows:Here, amount of heat transferred is Q, change in internal energy is and work done by the system is W.
Step 1
(a)Write the equation for temperature of state 1.Substitute for , , for and for .Write the equation for temperature of state 2.Substitute for , , for and for .
Explanation: The temperature of air at state 1 and state 2 is calculated by using volume of air, pressure of air and mass of air in cylinder.
Common mistakes: Use the ideal gas equation for temperature calculation instead of.
Hint for next step: Use the first law of thermodynamics and calculate the type of energy transfer..
Step 2
(b)Apply the first law of thermodynamics for air.The internal energy of air will not change due temperature and it will be constant during compression process. Process 1 to 2 is an isothermal process. The internal energy does not change in isothermal process.Therefore, the value of internal energy at state 1 and state 2 will remain same that is .Substitute for .All the compression work is converted into heat, since cylinder is not thermally insulated.Therefore, all heat is rejected into surrounding by mode of conduction.
Explanation: The relation between heat and work and the form of energy transfer occurred from state 1 to state 2 is obtained by applying first law of thermodynamics.
Answer
Part aThe temperature of air in state 2 is .
Answer
Part bThe form of energy transfer occurred from state 1 to state 2 is heat.
Concepts and reasonHeat:It is a form of energy exchanged between two systems and responsible for temperature difference between the systems.Work:Work is the amount of energy transferred between two systems or from a system to its surroundings.Internal energy:The total amount of kinetic and potential energy possessed by a system itself without any external influences is termed as internal energy.First Law of thermodynamics:For a closed thermodynamic system, the variation in internal energy
is equivalent to the difference in the heat energy 
supplied to the system and the work done 
by the system.Ideal gas law:An ideal gas with pressure p, temperature T, volume V and mass m obeys the following relation
Here, 
is the gas constant.The temperature of air at state 2 can be calculated by using the ideal gas relation. Then the type of energy transfer can be obtained by using the first law of thermodynamics.
Here, amount of heat transferred is Q, change in internal energy is 
and work done by the system is W.
FundamentalsThe relation for the first law of thermodynamics is as follows:
Step 1
of state 1.
Substitute 
for 
, 
, 
for 
and 
for 
.
Write the equation for temperature 
of state 2.
Substitute 
for 
, 
, 
for 
and 
for 
.
instead of
.
(a)Write the equation for temperature
Explanation: The temperature of air at state 1 and state 2 is calculated by using volume of air, pressure of air and mass of air in cylinder.
Common mistakes: Use the ideal gas equation for temperature calculation
Hint for next step: Use the first law of thermodynamics and calculate the type of energy transfer..
Step 2
The internal energy of air will not change due temperature and it will be constant during compression process. Process 1 to 2 is an isothermal process. The internal energy does not change in isothermal process.Therefore, the value of internal energy at state 1 and state 2 will remain same that is 
.Substitute 
for 
.
All the compression work is converted into heat, since cylinder is not thermally insulated.Therefore, all heat is rejected into surrounding by mode of conduction.
(b)Apply the first law of thermodynamics for air.
Explanation: The relation between heat and work and the form of energy transfer occurred from state 1 to state 2 is obtained by applying first law of thermodynamics.
Answer
is 
.
Part aThe temperature of air in state 2
Answer
Part bThe form of energy transfer occurred from state 1 to state 2 is heat.