Exercises of Thermodynamics
1. Choose the correct option.
i) A gas in a closed container is heated with 10J of energy, causing the lid of the container to rise 2m with 3N of force. What is the total change in energy of the system?
(A) 1 OJ
(B) 4J
(C) -1 OJ
(D) – 4J
ii) Which of the following is an example of the first law of thermodynamics?
(A) The specific heat of an object explains how easily it changes temperatures.
(B) While melting, an ice cube remains at the same temperature.
(C) When a refrigerator is unplugged, everything inside of it returns to room temperature after some time.
(D) After falling down the hill, a ball’s kinetic energy plus heat energy equals the initial potential energy.
iii) Efficiency of a Carnot engine is large when
(A) TH is large
(B) Tc is low
(C) TH – Tc is large
(D) TH – Tc is small
iv) The second law of thermodynamics deals with transfer of:
(A) work done
(B) energy
(C) momentum
(D) heat
v) During refrigeration cycle, heat is rejected by the refrigerant in the :
(A) condenser
(B) cold chamber
(C) evaporator
(D) hot chamber
2. Answer in brief.
i) A gas contained in a cylinder surrounded by a thick layer of insulating material is quickly compressed. (a) Has there been a transfer of heat? (b) Has work been done?
ii) Give an example of some familiar process in which no heat is added to or removed form a system, but the temperature of the system changes.
iii) Give an example of some familiar process in which heat is added to an object, without changing its temperature.
iv) What sets the limits on efficiency of a heat engine?
v) Why should a Carnot cycle have two isothermal two adiabatic processes?
3. Answer the questions.
i) A mixture of hydrogen and oxygen is enclosed in a rigid insulting cylinder. It is ignited by a spark. The temperature and the pressure both increase considerably. Assume that the energy supplied by the spark is negligible, what conclusions may be drawn by application of the first law of thermodynamics?
ii) A resistor held in running water carries electric current. Treat the resistor as the system (a) Does heat flow into the resistor? (b) Is there a flow of heat into the water? (c) Is any work done? (d) Assuming the state of resistance to remain unchanged, apply the first law of thermodynamics to this process.
iii) A mixture of fuel and oxygen is burned in a constant-volume chamber surrounded by a water bath. It was noticed that the temperature of water is increased during the process. Treating the mixture of fuel and oxygen as the system, (a) Has heat been transferred ? (b) Has work been done? (c) What is the sign of AU ?
iv) Draw a p-V diagram and explain the concept of positive and negative work. Give one example each.
v) A solar cooker and a pressure cooker both are used to cook food. Treating them as thermodynamic systems, discuss the similarities and differences between them.
4. A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from a volume of 5 litres to a volume of 10 litres. In doing so it absorbs 400 J of thermal energy from its surroundings. Determine the change in internal energy of system.
[Ans: 106.65 J]
5. A system releases 125 kJ of heat while 104 kJ of work is done on the system. Calculate the change in internal energy.
[Ans: ΔU= 21 kJ]
6. Efficiency of a Carnot cycle is 75%. If temperature of the hot reservoir is 727°C, calculate the temperature of the cold reservoir.
[Ans: 23°C]
7. A Carnot refrigerator operates between 250°K and 300°K. Calculate its coefficient of performance.
[Ans: 5]
8. An ideal gas is taken through an isothermal process. If it does 2000 J of work on its environment, how much heat is added to it?
[Ans: Zero]
9. An ideal monatomic gas is adiabatically compressed so that its final temperature is twice its initial temperature. What is the ratio of the final pressure to its initial pressure?
[Ans: 5.6]
10. A hypothetical thermodynamic cycle is shown in the figure. Calculate the work done in 25 cycles.
[Ans: 7.85 x 104 J]
11. The figure shows the V-T diagram for one cycle of a hypothetical heat engine which uses the ideal gas. Draw (a) the p–V diagram of the system.
[Ans: (a)] [Ans: (b)]
12. A system is taken to its final state from initial state in hypothetical paths as shown figure calculate the work done in each case.
[Ans: AB = 2.4 x 106 J, CD = 8 x 105 J, BC and DA zero, because constant volume change]