THE FIRST LAW OF THERMODYNAMICS AND PROCESSES

Question 1. State the equation which represents the first law of thermodynamics.

Question 2. In the equation representing the first law of thermodynamics, which of the following are considered as positive quantities:
(a) heat entering the system

(b) heat leaving the system

(c) work done on the system

(d) work done on the surroundings.

Question 3. In the equation representing the first law of thermodynamics, U2 represents :

(a) the internal energy before the process takes place (initial internal energy)

(b) the maximum internal energy

(c) the internal energy after the process has taken place (final internal energy).

Question 4. During a process on a closed system, the system receives 100 kJ of heat energy and the system delivers 20 kJ of work to the surroundings. Calculate the change of internal energy of the system during the process.

Question 5. A closed system contains 5kg of working fluid. During a process the system rejects 30 kJ of heat to the surroundings, and the internal energy of the working fluid decreases by 10 kJ kg^-1. Calculate the total amount of work done during the process, stating whether it is done on or by the system.

Question 6. In a constant volume process, 20 kJ of heat is added to a system and the temperature of the working fluid increases from 20°C to 50°C. If cv for the working fluid = 0.8 kJ kg^-1 K^-1, what is the mass of working fluid in the system?
7. For a thermodynamic process to take place:

(a) work must be performed on either the system or surroundings

(b) fluid must flow across the system boundary

(c) the working fluid in the system must undergo a change

(d) the internal energy of the system must change.

Question 8. State the equation used to calculate the work done in:

(a) a constant pressure process

(b) a polytropic process.

Question 9. A gas in a closed system expands from a given pressure and drives a piston over a given range. Rank the following expansions in terms of the magnitude of work output for a given increase in volume. Give the reason for your answer.
(a) isothermal expansion

(b) adiabatic expansion

(c) polytropic expansion.

Question 10. A gas in a cylinder is inititally at a pressure of 3 bar absolute. The gas expands according to the law p₁V₁^1.3 = p₂V₂^1.3 and drives the piston so that the cylinder volume increases from 0.2 m³ to 0.3 m³.

(a) Calculate:

(i) the pressure of the gas after expansion

(ii) the work done during the expansion.

(b) State whether the work is done on the gas in the cylinder or on the surroundings.

Question 11. A mass of air is compressed from p₁ = 2 bar abs, V₁ = 3 m³, T₁ = 30°C to a final condition of p₂ = 4 bar abs. Calculate the work done within these limits:

(a) under adiabatic conditions

(b) under polytropic conditions where n = 1.3

(c) under isothermal conditions.

For air: c_p = 1.005 kJ kg^-1 K^-1

c_v = 0.718 kJ kg^-1 K^-1