Physics · Textbook solutions

Thermodynamics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 34 questions

4. Thermodynamics — worked examples

10 q

Solved Examples

Worked · 10
  1. Solved Ex.4.1
    Calculate the internal energy of argon and oxygen.
  2. Solved Ex.4.2
    A gas enclosed in a cylinder is expanded to double its initial volume at a constant pressure of one atmosphere. How much work is done in this process?.
  3. Solved Ex.4.3
    1.0 kg of liquid water is boiled at 100 ∘^\circC and all of it is converted to steam. If the change of state takes place at the atmospheric pressure (1.01×1051.01 \times 10^{5} Pa), calculate (a) the energy transferred to the system, (b) the work done by the system during this change, and (c) the change in the internal energy of the system. Given, the volume of water changes from 1.0×10−31.0 \times 10^{-3} m3^{3} in liquid form to 1.6711.671 m3^{3} when in the form of steam. L=2256L = 2256 kJ/kg.
  4. Solved Ex.4.4
    104 kJ of work is done on certain volume of a gas. If the gas releases 125 kJ of heat, calculate the change in internal energy (in kJ) of the gas.
  5. Solved Ex.4.5
    0.5 mole of gas at temp 300 K expands isothermally from an initial volume of 2.0L to final volume of 6.0L. (a) What is the work done by the gas ? (R=8.319R = 8.319 J mol−1^{-1} K−1^{-1}), (b) How much heat is supplied to the gas?
  6. Solved Ex.4.6
    One mole of an ideal gas is initially kept in a cylinder with a movable frictionless and massless piston at pressure of 1.01MPa, and temperature 27∘^\circC. It is then expanded till its volume is doubled. How much work is done if the expansion is isobaric? (R=8.314R = 8.314 SI Units)
  7. Solved Ex.4.7
    An ideal gas of volume 1.0L is adiabatically compressed to (1/15)th(1/15)^{\text{th}} of its initial volume. Its initial pressure and temperature is 1.01×1051.01 \times 10^{5} Pa and 27∘^\circC respectively. Given CVC_{V} for ideal gas = 20.8J/mol.K and γ=1.4\gamma = 1.4. Calculate (a) final pressure, (b) work done, and (c) final temperature. (d) How would your answers change, if the process were isothermal ?
  8. Solved Ex.4.8
    Cyclic process: The total work done in the cyclic process shown in the Fig. 4.19 is −1000-1000 J. (a) What does the negative sign mean? (b) What is the change in internal energy and the heat transferred during this process. (c) What will happen when the direction of the cycle is changed?
  9. Solved Ex.4.9
    A cyclic process ABCA is shown in V-T diagram (Fig (a)). It is performed with a constant mass of ideal gas. How will this transform to a p-V digram?
  10. Solved Ex.4.10
    Carnot engine: A Carnot engine receives 2.0 kJ of heat from a reservoir at 500 K, does some work, and rejects some heat to a reservoir at 350 K. (a) How much work does it do? (b) how much heat is rejected. (c) what is its efficiency?

Exercises

24 q

Choose the correct option

Practice · 5
  1. Choose the correct option.
    Ex Q.1 (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 the internal energy of the system?
    1. A.
      10J
    2. B.
      4J
    3. C.
      -10J
    4. D.
      - 4J
  2. Ex Q.1 (ii)
    Which of the following is an example of the first law of thermodynamics?
    1. A.
      The specific heat of an object explains how easily it changes temperatures.
    2. B.
      While melting, an ice cube remains at the same temperature.
    3. C.
      When a refrigerator is unplugged, everything inside of it returns to room temperature after some time.
    4. D.
      After falling down the hill, a ball's kinetic energy plus heat energy equals the initial potential energy.
  3. Ex Q.1 (iii)
    Efficiency of a Carnot engine is large when
    1. A.
      THT_{H} is large
    2. B.
      TCT_{C} is low
    3. C.
      TH−TCT_{H} - T_{C} is large
    4. D.
      TH−TCT_{H} - T_{C} is small
  4. Ex Q.1 (iv)
    The second law of thermodynamics deals with transfer of:
    1. A.
      work done
    2. B.
      energy
    3. C.
      momentum
    4. D.
      mass
  5. Ex Q.1 (v)
    During refrigeration cycle, heat is rejected by the refrigerant in the :
    1. A.
      condenser
    2. B.
      cold chamber
    3. C.
      evaporator
    4. D.
      hot chamber

Answer in brief

Practice · 5
  1. Answer in brief.
    Ex Q.2 (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?
  2. Ex Q.2 (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.
  3. Ex Q.2 (iii)
    Give an example of some familiar process in which heat is added to an object, without changing its temperature.
  4. Ex Q.2 (iv)
    What sets the limits on efficiency of a heat engine?
  5. Ex Q.2 (v)
    Why should a Carnot cycle have two isothermal two adiabatic processes?

Answer the following questions

Practice · 5
  1. Answer the following questions.
    Ex Q.3 (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?
  2. Ex Q.3 (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.
  3. Ex Q.3 (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 ΔU\Delta U ?
  4. Ex Q.3 (iv)
    Draw a p-V diagram and explain the concept of positive and negative work. Give one example each.
  5. Ex Q.3 (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.

Solve the following

Practice · 9
  1. Ex Q.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.
  2. Ex Q.5
    A system releases 130 kJ of heat while 109 kJ of work is done on the system. Calculate the change in internal energy.
  3. Ex Q.6
    Efficiency of a Carnot cycle is 75%. If temperature of the hot reservoir is 727∘^\circC, calculate the temperature of the cold reservoir.
  4. Ex Q.7
    A Carnot refrigerator operates between 250K and 300K. Calculate its coefficient of performance.
  5. Ex Q.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?
  6. Ex Q.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?
  7. Ex Q.10
    A hypothetical thermodynamic cycle is shown in the figure. Calculate the work done in 25 cycles.
  8. Ex Q.11
    The figure shows the VV-TT diagram for one cycle of a hypothetical heat engine which uses the ideal gas. Draw the pp-VV diagram and pp-TT diagram of the system.
  9. Ex Q.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.