Question 1 |

Consider a mixture of two ideal gases, X and Y, with molar masses \bar{M}_X=10kg/kmol and \bar{M}_Y=20kg/kmol , respectively, in a container. The total
pressure in the container is 100 kPa, the total volume of the container is 10m^3
and the temperature of the contents of the container is 300 K. If the mass of
gas-X in the container is 2 kg, then the mass of gas-Y in the container
is ____ kg. (Rounded off to one decimal place)

Assume that the universal gas constant is 8314 J \;kmol^{-1}K^{-1}

Assume that the universal gas constant is 8314 J \;kmol^{-1}K^{-1}

2 | |

4 | |

6 | |

8 |

Question 1 Explanation:

By gas law

\mathrm{Pv}=\mathrm{nRT}

where \mathrm{n}= total value of gas in container

\begin{aligned} 100 \times 10 & =n \times 8.314 \times 300 \\ n & =0.4 \end{aligned}

and \mathrm{n}=\mathrm{n}_{\mathrm{x}}+\mathrm{n}_{\mathrm{y}}

Or, 0.4=\frac{m_{x}}{M_{x}}+\frac{m_{y}}{M_{y}}=\frac{2}{10}+\frac{m_{y}}{20} or, m_{y}=4 \mathrm{~kg}

Question 2 |

Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is
massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder is air
(considered as a perfect gas), with \gamma being the ratio of the specific heat at constant pressure to
the specific heat at constant volume for air. The piston is initially located at a position L_1 . The
initial pressure of the air inside the cylinder is P_1 \gt \gt P_0 , where P_0 is the atmospheric pressure.
The stop S_1 is instantaneously removed and the piston moves to the position L_2 , where the
equilibrium pressure of air inside the cylinder is P_2 \gt \gt P_0 .

What is the work done by the piston on the atmosphere during this process?

What is the work done by the piston on the atmosphere during this process?

0 | |

P_0A(L_2-L_1) | |

P_1AL_1 \ln \frac{L_1}{L_2} | |

\frac{(P_2L_2-P_1L_1)A}{(1-\gamma )} |

Question 2 Explanation:

Initial volume \mathrm{V}_{1}=\mathrm{L}_{1} \times \mathrm{A}

Final volume V_{2}=L_{2} \times A

Work done by atmospheric air =\int_{V_{1}}^{V_{2}} P d v

\begin{aligned} & =P_{0} \int_{V_{1}}^{V_{2}} d V \\ & =P_{0}\left(L_{2} A-L_{1} A\right) \\ & =P_{0} A\left(L_{2}-L_{1}\right) \end{aligned}

Question 3 |

Which one of the following statements is FALSE?

For an ideal gas, the enthalpy is independent of pressure. | |

For a real gas going through an adiabatic reversible process, the process equation is given by PV^\gamma = constant, where P is the pressure, V is the volume and \gamma is the ratio of the specific heats
of the gas at constant pressure and constant volume. | |

For an ideal gas undergoing a reversible polytropic process PV^{1.5} = constant, the equation
connecting the pressure, volume and temperature of the gas at any point along the process is \frac{P}{R}=\frac{mT}{V} where R is the gas constant and m is the mass of the gas. | |

Any real gas behaves as an ideal gas at sufficiently low pressure or sufficiently high
temperature. |

Question 3 Explanation:

Ideal gas follow the adiabatic equation \mathrm{PV}^{\gamma}=\mathrm{C} and also follow the gas law P V=m R T

Any real gas at low pressure and high temperature follow gas law, e.g. Air conditioning system.

Real gas follow Van der waal's gas equation for an adiabatic process as

\left(P+\frac{n^{2} a}{V^{a}}\right)(V-n b)^{\top}=k

where

\begin{aligned} & \mathrm{T}=\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}+1 \\ & \mathrm{k}=\mathrm{nRZ} \end{aligned}

Enthalpy of an ideal gas is independent of pressure at constant temperature and the internal energy of an ideal gas is independent of volume at constant temperature.

Any real gas at low pressure and high temperature follow gas law, e.g. Air conditioning system.

Real gas follow Van der waal's gas equation for an adiabatic process as

\left(P+\frac{n^{2} a}{V^{a}}\right)(V-n b)^{\top}=k

where

\begin{aligned} & \mathrm{T}=\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}+1 \\ & \mathrm{k}=\mathrm{nRZ} \end{aligned}

Enthalpy of an ideal gas is independent of pressure at constant temperature and the internal energy of an ideal gas is independent of volume at constant temperature.

Question 4 |

A heat engine extracts heat (Q_H) from a thermal reservoir at a temperature of
1000 K and rejects heat (Q_L) to a thermal reservoir at a temperature of 100 K,
while producing work (W). Which one of the combinations of (Q_H,Q_L,W) given is allowed?

Q_H=2000J, Q_L=500J, W=1000J | |

Q_H=2000J, Q_L=750J, W=1250J | |

Q_H=6000J, Q_L=500J, W=5500J | |

Q_H=6000J, Q_L=600J, W=5500J |

Question 4 Explanation:

For a reversible engine, the rate of heat rejection
is minimum.

For process to be feasible

\oint \frac{dQ}{T}\leq 0

for option (b) \oint \frac{dQ}{T}=\frac{Q_H}{T_1}-\frac{Q_2}{T_2}=\frac{2000}{1000}-\frac{750}{100} \lt 0

So cyclic process is possible.

For process to be feasible

\oint \frac{dQ}{T}\leq 0

for option (b) \oint \frac{dQ}{T}=\frac{Q_H}{T_1}-\frac{Q_2}{T_2}=\frac{2000}{1000}-\frac{750}{100} \lt 0

So cyclic process is possible.

Question 5 |

Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as
shown in the figure.

The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:

?? P_1=100kPa, \rho _1=1.2kg/m^3,u_1=400m/s

The duct cross-sectional area at Location 2 is given by A_2=2A_1, where A_1 denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity u_2 and pressure P_2 at Location 2 is TRUE?

The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:

?? P_1=100kPa, \rho _1=1.2kg/m^3,u_1=400m/s

The duct cross-sectional area at Location 2 is given by A_2=2A_1, where A_1 denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity u_2 and pressure P_2 at Location 2 is TRUE?

u_2 \lt u_1, P_2 \lt P_1 | |

u_2 \lt u_1, P_2 \gt P_1 | |

u_2 \gt u_1, P_2 \lt P_1 | |

u_2 \gt u_1, P_2 \gt P_1 |

Question 5 Explanation:

Step -1:
First identify type of flow - Subsonic or
Supersonic by finding out Mach number

Mach no at start of flow

M_a=\frac{u_1}{C_1},\; where, \; C_1=\sqrt{\gamma RT_1}

u_1 is velocity of gas

C_1 is velocity of sound

\begin{aligned} P_1 &=\rho _1RT_1 \\ T_1&= \frac{P_1}{\rho _1R}=\frac{100}{1.2 \times 0.287}=290.36K\\ C_1 &=\sqrt{1.4 \times 287 \times 290.36} \\ &= 341.56 m/sec\\ Ma_1 &=\frac{400}{341.56}=1.017 \end{aligned}

Flow is supersonic flow. Hence, diverging duct is nozzle so u_2 \gt u_1 and P_2 \lt P_1 .

Mach no at start of flow

M_a=\frac{u_1}{C_1},\; where, \; C_1=\sqrt{\gamma RT_1}

u_1 is velocity of gas

C_1 is velocity of sound

\begin{aligned} P_1 &=\rho _1RT_1 \\ T_1&= \frac{P_1}{\rho _1R}=\frac{100}{1.2 \times 0.287}=290.36K\\ C_1 &=\sqrt{1.4 \times 287 \times 290.36} \\ &= 341.56 m/sec\\ Ma_1 &=\frac{400}{341.56}=1.017 \end{aligned}

Flow is supersonic flow. Hence, diverging duct is nozzle so u_2 \gt u_1 and P_2 \lt P_1 .

There are 5 questions to complete.

Hello,

It would have been good if options weren’t provided for numerical type questions.

Can you provide the same for XE-E,and XE-D