Thermodynamics

Question 1
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      Thermodynamic System and Processes
Question 1 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 2
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      Thermodynamic System and Processes
Question 2 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 3
Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume c_v is equal to 750 \; Jkg^{-1}K^{-1}. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be ______ bar (in integer).
A
1
B
2
C
3
D
4
GATE ME 2022 SET-2      First Law, Heat, Work and Energy
Question 3 Explanation: 
m = 1 kg, P_1 = 1 \;bar, T_1 = 300 \;K

\begin{aligned} V &= \text{Constant} \\ W_{expansion}&= 0\\ C_V &=750\frac{J}{kgK}=0.75\frac{kJ}{kgK} \\ W_{stirrer}&= 225kJ\;\;\;(-ve \;\; work)\\ P_2&=? \\ \therefore W&= W_{expansion}+W_{stirrer}\\ &=0-225=-225kJ \end{aligned}
Using Ist law of thermodynamics
\begin{aligned} Q-W&=dU=mc_v(T_2-T_1)\\ 0-(-225)&=1 \times 0.75(T_2-300)\\ T_2&=600K\\ \therefore \frac{P_2}{P_1}&=\frac{T_2}{T_1}\\ P_2&=\frac{600}{300} \times 1 =2\; bar \end{aligned}
Question 4
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      Thermodynamic System and Processes
Question 4 Explanation: 
Intensive property -> Density

Mass, energy and volume are extensive properties.
Question 5
An engine running on an air standard Otto cycle has a displacement volume 250 cm^3 and a clearance volume 35.7 cm^3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).
A
4811
B
1254
C
2589
D
2547
GATE ME 2022 SET-1      IC Engine
Question 5 Explanation: 


\begin{aligned} V_S&=250cm^3\\ V_C&=35.7 cm^3\\ T_1&=300K\\ P_1&=100kPa\\ Q_S&=800kJ/kg\\ C_v&=0.718kJ/kgK\\ \gamma &=1.4\\ P_3&=\_\_\_kPa\\ \frac{T_2}{T_1}&=\left ( \frac{P_2}{P_1} \right )^{\frac{\gamma -1}{\gamma }}=\left ( \frac{V_1}{V_2} \right )^{\gamma -1}=\left ( \frac{V_S+V_C}{V_C} \right )^{\gamma -1}\\ \frac{T_2}{300}&=\left ( \frac{P_2}{100} \right )^{\frac{1.4-1}{1.4 }}=\left ( \frac{250+35.7}{35.7} \right )^{1.4 -1}\\ T_2&=689.31K\\ P_2&=1838.82kPa\\ Q_S&=c_v \times (T_3-T_2)\\ 800&=0.718(T_3-689.31)\\ T_3&=1803.516K\\ &\text{For Process 2-3(Volume is constant)}\\ \frac{P_3}{P_2}&=\frac{T_3}{T_2}\\ P_3&=\frac{1803.516}{689.31} \times 1838.82\\ P_3&=4811kPa \end{aligned}
Question 6
In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is 400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser is ________ kJ/kg (round off to 2 decimal places).
A
2624.37
B
1225.36
C
3625.25
D
1475.36
GATE ME 2022 SET-1      Power System
Question 6 Explanation: 


\begin{aligned} W_{HPT}&=400kJ/kg\\ W_{LPT}&=850kJ/kg\\ W_{P}&=15kJ/kg\\ \eta &=0.35=\frac{W_{net}}{Q_S}\\ Q_S&=3859.375 kJ/kg\\ \therefore \; W_{net}&=Q_S-Q_R\\ Q_R&=3859.375-1235\\ Q_R&=2624.37 kJ/kg \end{aligned}
Question 7
A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m^3 to a final volume of 2.5 m^3. The polytropic index is given by n = 1.2. The absolute value of the work done during the process is _______ kJ (round off to 2 decimal places).
A
408.92
B
215.58
C
852.36
D
789.14
GATE ME 2022 SET-1      First Law, Heat, Work and Energy
Question 7 Explanation: 
Polytropic process]
\begin{aligned} P_1 &= 110 kPa,\\ V_1&= 5m^3,\\ V_2&=2.5 m^3,\\ n&=1.2\\ \Rightarrow \; P_1V_1^n&=P_2V_2^n\\ P_2&=P_1\left ( \frac{V_1}{V_2} \right )^n\\ &=110 \times \left ( \frac{5}{2.5} \right )^{1.2}\\ P_2&=252.71 kPa\\ W&=\frac{P_1V_1=P_2V_2}{n-1}\\ &=\frac{110 \times 5-252.71 \times 2.5}{1.2-1}\\ W&=-408.92kJ\\ |W|&=408.92kJ \end{aligned}
Question 8
The Clausius inequality holds good for
A
any process
B
any cycle
C
only reversible process
D
only reversible cycle
GATE ME 2022 SET-1      Availability and Irreversibility
Question 8 Explanation: 
The Clausius inequality holds good for any cycle.
\oint \frac{dQ}{T}=0\Rightarrow Reversible cycle
\oint \frac{dQ}{T} \lt 0\Rightarrow Irreversible cycle
\oint \frac{dQ}{T} \gt 0\Rightarrow Impossible cycle
Question 9
An adiabatic vortex tube, shown in the figure given below is supplied with 5 kg/s of air (inlet 1) at 500 kPa and 300 K. Two separate streams of air are leaving the device from outlets 2 and 3. Hot air leaves the device at a rate of 3 kg/s from outlet 2 at 100 kPa and 340 K, and 2 kg/s of cold air stream is leaving the device from outlet 3 at 100 kPa and 240 K.

Assume constant specific heat of air is 1005 J/kg.K and gas constant is 287 J/kg.K. There is no work transfer across the boundary of this device. The rate of entropy generation is ________kW/K (round off to one decimal place).
A
1.2
B
4.3
C
2.2
D
3.8
GATE ME 2021 SET-2      Second Law, Carnot Cycle and Entropy
Question 9 Explanation: 


\begin{aligned} \left(\frac{d S}{d t}\right)_{C . V} &=\dot{S}_{i}+\dot{S}_{g e n}-\dot{S}_{\theta} \\ \dot{S}_{\text {gen }} &=\dot{S}_{e}-\dot{S}_{i} \\ &=\dot{m}_{2} s_{2}+\dot{m}_{3} s_{3}-\dot{m}_{1} s_{1} \\ &=3\left(s_{2}-s_{1}\right)+2\left(s_{3}-s_{1}\right) \\ &=3 \times 0.587+2(0.237) \\ &=2.235 \mathrm{~kW} / \mathrm{K} \simeq 2.2 \mathrm{~kW} / \mathrm{K} \end{aligned}
Question 10
Consider the open feed water heater (FWH) shown in the figure given below:

Specific enthalpy of steam at location 2 is 2624 kJ/kg, specific enthalpy of water at location 5 is 226.7 kJ/kg and specific enthalpy of saturated water at location 6 is 708.6 kJ/kg. If the mass flow rate of water entering the open feed water heater (at location 5) is 100 kg/s then the mass flow rate of steam at location 2 will be kg/s (round off to one decimal place).
A
25.2
B
45.6
C
62.3
D
18.4
GATE ME 2021 SET-2      Power System
Question 10 Explanation: 




\begin{aligned} 100 h_{5}+(x-100) h_{2} &=x h_{6} \\ 100 \times 226.7+(x-100) 2624&=708.6 x \\ 22670+2624 x-262400 &=708.6 x \\ 2624 x-708.6 x &=239730 \\ 1915.4 x &=239730 \\ x &=125.159 \simeq 125.2 \mathrm{~kg} / \mathrm{s} \end{aligned}
Mass flow rate at state 2(x-100)=25.2 \mathrm{~kg} / \mathrm{s}


There are 10 questions to complete.

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