FIRST LAW OF THERMODYNAMICS 221
dharm
/M-therm/Th4-7.pm5- In the compression stroke of an internal-combustion engine the heat rejected to the cooling water is
45 kJ/kg and the work input is 90 kJ/kg. Calculate the change in internal energy of the working fluid
stating whether it is a gain or a loss. [Ans. 45 kJ/kg (gain)] - 85 kJ of heat are supplied to a system at constant volume. The system rejects 90 kJ of heat at constant
pressure and 20 kJ of work is done on it. The system is brought to its original state by adiabatic process.
Determine the adiabatic work. Determine also the value of internal energy at all end states if initial value
is 100 kJ. [Ans. W = 15 kJ ; U 1 = 100 kJ, U 2 = 185 kJ ; U 3 = 115 kJ] - A closed system undergoes a reversible process at a constant pressure process of 3.5 bar and its volume
changes from 0.15 m^3 to 0.06 m^3. 25 kJ of heat is rejected by the system during the process. Determine the
change in internal energy of the system. [Ans. 6.5 kJ (increase)] - An air compressor takes in air at 10^5 Pa and 27°C having volume of 1.5 m^3 /kg and compresses it to 4.5 × 10^5 Pa.
Find the work done, heat transfer and change in internal energy if the compression is isothermal.
[Ans. – 225 kJ ; – 225 kJ ; ∆U = 0] - A cylinder fitted with piston contains 0.2 kg of N 2 at 100 kPa and 30°C. The piston is moved compressing N 2
until the pressure becomes 1 MPa and temperature becomes 150°C. The work done during the process is
20 kJ. Determine the heat transferred from N 2 to the surroundings. Take cv = 0.75 kJ/kg K for N 2.
[Ans. – 2 kJ] - A closed system consisting of 1 kg of gaseous CO 2 undergoes a reversible process at constant pressure
causing a decrease of 30 kJ in internal energy. Determine the work done during the process. Take cp = 840
J/kg°C and cv = 600 J/kg°C. [Ans. – 12 kJ] - The specific heat at constant pressure of one kg fluid undergoing a non-flow constant pressure process is
given by
cp = 2.5^40
20
+
+L
N
MO
Q
T P kg/kg°C
where T is in °C.
The pressure during the process is maintained at 2 bar and volume changes from 1 m^3 to 1.8 m^3 and
temperature changes from 50°C to 450°C. Determine :
(i) Heat added (ii) Work done
(iii) Change in internal energy (iv) Change in enthalpy.
[Ans. (i) 1076 kJ ; (ii) 160 kJ ; (iii) 916 kJ ; (iv) 1076 kJ]- 1 kg of nitrogen (molecular weight 28) is compressed reversibly and isothermally from 1.01 bar, 20°C to
4.2 bar. Calculate the work done and the heat flow during the process. Assume nitrogen to be a perfect gas.
[Ans. W = 124 kJ/kg ; Q = – 124 kJ/kg] - Air at 1.02 bar, 22°C, initially occupying a cylinder volume of 0.015 m^3 , is compressed reversibly and
adiabatically by a piston to a pressure of 6.8 bar. Calculate :
(i) The final temperature (ii) The final volume
(iii) The work done on the mass of air in the cylinder. [Ans. (i) 234.5°C, (ii) 0.00388 m^3 ; (iii) 2.76 kJ] - 1 kg of a perfect gas is compressed from 1.1 bar, 27°C according to a law pv1.3 = constant, until the pressure
is 6.6. bar. Calculate the heat flow to or from the cylinder walls,
(i) When the gas is ethane (molecular weight 30), which has
cp = 1.75 kJ/kg K.
(ii) When the gas is argon (molecular weight 40), which has
cp = 0.515 kJ/kg K. [Ans. (i) 84.5 kJ/kg, (ii) – 59.4 kJ/kg] - 1 kg of air at 1 bar, 15°C is compressed reversibly and adiabatically to a pressure of 4 bar. Calculate the final
temperature and the work done on the air. [Ans. 155°C ; 100.5 kJ/kg] - A certain perfect gas is compressed reversibly from 1 bar, 17°C to a pressure of 5 bar in a perfectly
thermally insulated cylinder, the final temperature being 77°C. The work done on the gas during the
compression is 45 kJ/kg. Calculate γ, cv, R and the molecular weight of the gas.
[Ans. 1.132 ; 0.75 kJ/kg K ; 0.099 kJ/kg K ; 84]