Thermodynamics and Gas Laws

Directions: Carry One Mark Each.

An air-standard diesel cycle consists of the following processes:

1–2: Air is compressed isentropically. 2–3: Heat is added at constant pressure. 3–4: Air expands isentropically to the original volume. 4–1: Heat is rejected at constant volume. If ^$\gamma$ and T respectively denote the specific heat ratio and temperature, then the efficiency of the cycle is

In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150 kPa and 350 K. The temperature at station Q is 300 K. The following are the properties and relations pertaining to air: Specific heat at constant pressure, C_p = 1.005 kJ/kgK; Specific heat at constant volume, C_v = 0.718 kJ/kgK; Characteristic gas constant, R = 0.287 kJ/kgK Enthalpy, h = c_p T Internal energy, u = C_v T

If the pressure at station Q is 50 kPa, the change in entropy (s_Q - s_P ) in kJ/kgK is

In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150 kPa and 350 K. The temperature at station Q is 300 K. The following are the properties and relations pertaining to air: Specific heat at constant pressure, C_p = 1.005 kJ/kgK; Specific heat at constant volume, C_v = 0.718 kJ/kgK; Characteristic gas constant, R = 0.287 kJ/kgK Enthalpy, h = c_p T Internal energy, u = C_v T

If the air has to flow from station P to station Q, the maximum possible value of pressure in kPa at station Q is close to

The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging-diverging nozzle of exit area 0.005 m² is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively.

The density of air (in kg/m³) at the nozzle exit is

The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging-diverging nozzle of exit area 0.005 m² is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively.

The mass flow rate of air through the nozzle in kg/s is

A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressor is designated as state 1 and state 2, respectively. Potential and kinetic energy changes are to be ignored. The following notations are used:

V = specific volume and P = pressure of the gas The specific work required to be supplied to the compressor for this gas compression process is

In an air-standard Otto cycle, the compression ratio is 10. The condition at the beginning of the compression process is 100 kPa and 27°C. Heat added at constant volume is 1500 kJ/kg, while 700 kJ/kg of heat is rejected during the other constant volume process in the cycle. Specific gas constant for air = 0.287 kJ/kgK. The mean effective pressure (in kPa) of the cycle is

The inlet and the outlet conditions of stream for an adiabatic steam turbine are indicated in the notations as usually followed.

Assume the above turbine to be part of a simple Rankine cycle. The density of water at the inlet to the pump is 1000 kg/m³. Ignoring kinetic and potential energy effects, the specific work (in kJ/kg) supplied to the pump is

2 moles of oxygen are mixed adiabatically with another 2 moles of oxygen in mixing chamber, so that the final total pressure and temperature of the mixture becomes same as those of the individual constituents at their initial states. The universal gas constant is given as R. The change in entropy due to mixing, per mole of oxygen, is given by