# Thermodynamic System and Processes

 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 $J \;kmol^{-1}K^{-1}$
 A 2 B 4 C 6 D 8
GATE ME 2023   Thermodynamics
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
Which one of the following statements is FALSE?
 A For an ideal gas, the enthalpy is independent of pressure. B 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. C 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. D Any real gas behaves as an ideal gas at sufficiently low pressure or sufficiently high temperature.
GATE ME 2023   Thermodynamics
Question 2 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.

 Question 3
At steady state, $500 kg/s$ of steam enters a turbine with specific enthalpy equal to $3500 kJ/ kg$ and specific entropy equal to $6.5 kJ \dot kg^{-1}\dot K^{-1}$. It expands reversibly in the turbine to the condenser pressure. Heat loss occurs reversibly in the turbine at a temperature of $500 K$. If the exit specific enthalpy and specific entropy are $2500 kJ/kg$ and $6.3 kJ\dot kg^{-1} \dot K^{-1}$, respectively, the work output from the turbine is ________ MW (in integer).
 A 320 B 650 C 275 D 450
GATE ME 2022 SET-2   Thermodynamics
Question 3 Explanation:
Mass flow rate of stem $\dot{m}=500kg/s$
$h_1=300 kJ/kg$
$S_1=6.5 kJ/kgL$
$h_2=2500kJ/kg$
$S_2=6.3 kJ/kgK$ Surrounding temperature $T_o=500 K$
Work output from turbine
\begin{aligned} W_T&=(h_1-h_2)-T_o(S_1-S_2)\\ &=(3500-2500)-500(6.5-6.3)\\ &=1000-100\\ &=900 kJ/kg \end{aligned}
Power output of turbine
\begin{aligned} P&=\frac{W_T}{kg} \times \dot{m}\\ &=900 \times 500\\ &=450000 kW\\ &=450 MW \end{aligned}
 Question 4
A rigid tank of volume of 8 $m^3$ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained at 600 kPa and 306 K, respectively. The filling of the tank begins by opening the valve and the process ends when the tank pressure is equal to the pipeline pressure. During the filling process, heat loss to the surrounding is 1000 kJ. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kg.K and 0.718 kJ/kg.K, respectively. Neglect changes in kinetic energy and potential energy.
The final temperature of the tank after the completion of the filling process is _________ K (round off to the nearest integer).
 A 395 B 254 C 355 D 125
GATE ME 2022 SET-2   Thermodynamics
Question 4 Explanation: Initially the tank is completely evacuated ($m_1 = 0$)
After the gas is filled with tank, the gas pressure in the tank is 600 kPa.
Heat lost to surroundings (Q) = 1000 kJ
$c_p=1.005 KJ/kgK$
$c_v=0.718KJ/kgK$
$R=c_p-c_v=0.287 kJ/kgK$
(Changes in KE and PE are negligible)
Final temperature of gas $T_f=?$
m = mass of gas entering to tank
The energy balance equation is energy carried by gas in the pipe = energy of gas in the rigid tank + Heat lost to surrounding
\begin{aligned} mh_i&=mu_f+Q\\ h_i&=u_f+\frac{Q}{m}\\ C+pT_i&=C_vT_f+\frac{1000}{\frac{16724.73868}{T_f}} \end{aligned}
Mass of gas in the tank
\begin{aligned} m=\frac{P_fV_f}{RT_f}\\ &=\frac{600(8)}{0.287(T_f)}\\ &=\frac{16724.73868}{T_f}\\ 1.005(306)&=0.718T_f+\frac{1000T_f}{16724.73868}\\ &=0.718T_f+0.05979T_f\\ &=0.77779T_f\\ \therefore \; T_f&=\frac{1.005 \times 306}{0.77779}\\ &=395.389K\approx 395K \end{aligned}
 Question 5
Which one of the following is an intensive property of a thermodynamic system?
 A Mass B Density C Energy D Volume
GATE ME 2022 SET-2   Thermodynamics
Question 5 Explanation:
Intensive property -> Density

Mass, energy and volume are extensive properties.

There are 5 questions to complete.

### 5 thoughts on “Thermodynamic System and Processes”

1. great work,user friendly site, but one suggestion for some questions (like q1) ,please add some explanation like formula name or concept usedlike that 👍👏

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4. 5. 