




Molar heat capacities of a diatomic ideal gas: 


C_{v} = 12.5J(molK)^{1}
and C_{p} = 20.8J(molK)^{1} 



1. 

Explain briefly: 

a) 
why a gas exerts a pressure 

b) 
why the pressure increases with temperature. 



2. 

In terms of molecular motion, explain the how evaporation can
cause cooling. 


Give an example of a practical use of the phenomenon of cooling
by evaporation. 



3. 

In terms of molecular motion, explain why compressing a gas
causes its temperature to increase. 


Give an example of a practical use of the increase in
temperature caused by compressing a gas. 



4. 

Two cylinders (of negligible heat capacity) each contain
1mol of a gas. 


The gas in each cylinder is heated to increase its temperature
by 1K. 


One cylinder is heated at constant volume and the other is
heated at constant pressure. 


By considering the quantities of heat supplied to the two
cylinders, prove that the following relation is true: 


C_{p}  C_{V}
= R 


where C_{p} is the molar heat capacity at constant
pressure, C_{V} is the molar heat capacity at constant
volume and R is the universal gas constant. 



5. 

Two experiments were done attempting to verify the
BoyleMarriotte law. 


The graphs below were obtained. 





In each case the broken line indicates (approximately) the
expected result. 


Unfortunately, neither of these graphs verifies the law. 


What is the most probable reason for the failure of each
experiment? 



6. 

Two moles of an ideal gas are heated at a constant pressure of
10^{5}Pa. 


The temperature of the gas increases from 293K
to 313K. 


Calculate: 

a) 
the quantity of thermal energy supplied during the heating
process 

b) 
the change in internal energy of the gas 

c) 
the work done by the gas during expansion 

d) 
the change in volume of the gas. 



7. 

20mols of an ideal gas are in a
cylinder of initial volume 0.5m^{3}
at a temperature of 27°C. 


The gas is supplied with 10000J
of heat at constant pressure. 


Calculate: 

a) 
the final temperature of the gas 

b) 
the final volume of the gas 

c) 
the change in internal energy of the gas 



8. 

A cylinder has a volume, V, and contains 2.00×10^{2}mols
of oxygen (behaving as an ideal gas) at 20°C and 1.00×10^{5}Pa. 


The gas is compressed rapidly into a volume V/25. 


The pressure of the gas increases to 9.06×10^{6}Pa 

a) 
The volume of the has gas been made 25
times smaller. 


Why has the pressure increased by more than 25 times? 

b) 
Calculate the temperature of the compressed gas assuming that no
thermal energy entered of left the gas during the compression. 

c) 
Calculate the volume of the cylinder, V. 

d) 
If the internal energy of 1mol
of oxygen is increased by 12.5J,
then the temperature of the gas will increase by
1K. 


Use this fact to calculate the work done during the compression. 



9. 

Draw diagrams to represent: 

a) 
a heat engine 

b) 
a heat pump (or fridge) 


On the diagrams, label the work done, w, the energy taken from
the source, Q_{1} and energy given to the sink, Q_{2}. 



10. 

Referring to your diagrams of the previous question, write down
expressions for the thermodynamic efficiency of: 

a) 
a heat engine 

b) 
a heat pump 

c) 
a fridge 



11. 

A heat engine is used to lift a mass of 200kg. 


The mass moves 10m vertically
upwards. 


The temperature of the source of the heat engine is 1000K
and the heat sink is the atmosphere at 293K. 


Ignoring friction in the engine, pulleys etc, calculate the
minimum quantity of thermal energy needed to lift the mass. 