# Refrigeration and Air-conditioning

 Question 1
In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to 250 kJ/kg. The exit of the compressor is superheated at condenser pressure with specific enthalpy equal to 300 kJ/kg. At the condenser exit, the refrigerant is throttled to the evaporator pressure. The coefficient of performance (COP) of the cycle is 3. If the specific enthalpy of the saturated liquid at evaporator pressure is 50 kJ/kg, then the dryness fraction of the refrigerant at entry to evaporator is __
 A 0.2 B 0.25 C 0.3 D 0.35
GATE ME 2022 SET-2      Heat Pumps and Cycles
Question 1 Explanation:
Given data,
Saturated vapour refrigerant enters to compressor COP = 3

Specific liquid enthalpy of refrigerant corresponding to evaporator pressure $(h_f)_{P_1}=50 kJ/kg$.
Dryness fraction of refrigerant of entry to evaporator $(x_4)=?$
\begin{aligned} COP &=\frac{h_1-h_4}{h_2-h_1} \\ 3 &=\frac{250-h_4}{300-250} \\ h_4&=100kJ/kg \\ \text{But } h_4&=(h_f)_{P_1}+x_4(h_{f_g})_{P_1} \\ (h_{f_g})_{P_1}&= (h_{g})_{P_1} - (h_{f_1})_{P_1}\\ \Rightarrow h_{fg}&=250-50=200kJ/kg \\ 100&=50+x_4 \times 200 \\ \Rightarrow x_4&=0.25 \end{aligned}
 Question 2
Ambient pressure, temperature, and relative humidity at a location are 101 kPa, 300 K, and 60%, respectively. The saturation pressure of water at 300 K is 3.6 kPa. The specific humidity of ambient air is _______g/kg of dry air.
 A 21.4 B 35.1 C 21.9 D 13.6
GATE ME 2021 SET-2      Properties of Moist Air
Question 2 Explanation:
\begin{aligned} \phi &=0.6 \\ \frac{P_{v}}{P_{v s}} &=0.6 \\ P_{v s} &=3.6 \mathrm{kPa} \\ P_{v} &=0.6 \times 3.6 \mathrm{kPa} \\ P_{v} &=2.16 \mathrm{kPa} \\ \omega &=0.622\left(\frac{P_{V}}{P-P_{V}}\right) \\ &=0.622\left(\frac{2.16}{101-2.16}\right)\\ &=0.01358 \mathrm{~kg} \text { of water vapour/kg of dry air }\\ &=13.58 \mathrm{~g} / \mathrm{kg} \text { of dry air } \end{aligned}
 Question 3
A rigid tank of volume $50\; m^3$ contains a pure substance as a saturated liquid vapour mixture at 400 kPa. Of the total mass of the mixture, 20% mass is liquid and 80% mass is vapour. Properties at 400 kPa are : $T_{sat}=143.61^{\circ}C,\; v_f=0.001084\; m^3/kg, v_g=0.46242\; m^3/kg$. The total mass of liquid vapour mixture in the tank is _______kg (round off to the nearest integer).
 A 135 B 115 C 98 D 175
GATE ME 2021 SET-2      Psychrometric Process
Question 3 Explanation:
\begin{aligned} V_{\text {total }} &=v_{l}+v_{v} \\ &=v_{f} \times m_{l}+v_{g} \times m_{v} \\ 50 &=0.001084 \times 0.2 \mathrm{~m}+0.46242 \times 0.8 \mathrm{~m} \\ m &=135.08 \mathrm{~kg}=135 \mathrm{~kg} \end{aligned}
 Question 4
Consider an ideal vapour compression refrigeration cycle working on R-134a refrigerant. The COP of the cycle is 10 and the refrigeration capacity is 150 kJ/kg. The heat rejected by the refrigerant in the condenser is _______kJ/kg (round off to the nearest integer).
 A 125 B 185 C 215 D 165
GATE ME 2021 SET-2      Vapor and Gas Refrigeration
Question 4 Explanation:
\begin{aligned} \mathrm{RE} &=150 \mathrm{~kJ} / \mathrm{kg} \\ \mathrm{COP} &=10 \\ \mathrm{COP} &=\frac{Q_{L}}{W_{i n}}\\ \Rightarrow\qquad W_{\text {in }} &=15 \mathrm{~kJ} / \mathrm{kg} \\ Q_{\mathrm{H}}=Q_{\mathrm{C}} &=Q_{L}+W_{\text {in }} \\ &=150+15 \\ &=165 \mathrm{~kJ} / \mathrm{kg} \end{aligned}

 Question 5
An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the quality of the indoor air, the intake duct supplies a mixture of fresh air with a cold air stream. The two streams are mixed in an insulated mixing chamber located upstream of the intake duct. Cold air enters the mixing chamber at $5^{\circ} C$, 105 kPa with a volume flow rate of 1.25 $m^3/s$ during steady state operation. Fresh air enters the mixing chamber at $34^{\circ}C$ and 105 kPa. The mass flow rate of the fresh air is 1.6 times of the cold air stream. Air leaves the room through the exit duct at $24^{\circ}C$.

Assuming the air behaves as an ideal gas with $c_p= 1.005 \;\; kJ/kg.K$ and $R= 0.287 kJ/kg.K$, the rate of heat gain by the air from the room is ________kW(round off to two decimal places).
 A 4.96 B 2.25 C 6.25 D 8.12
GATE ME 2021 SET-1      Psychrometric Process
Question 5 Explanation:
1: Cold air
2: Hot air
\begin{aligned} P_{1} V_{1} &=\dot{m}_{1} R T_{1} \\ 105 \times 1.25 &=\dot{m}_{1} \times 0.287 \times 278 \\ \dot{m}_{1} &=1.645 \mathrm{~kg} / \mathrm{sec} \\ \dot{m}_{2} &=1.6 \times 1.645=2.632 \mathrm{~kg} / \mathrm{sec} \\ \dot{m}_{3} &=4.277 \mathrm{~kg} / \mathrm{sec} \end{aligned}
After mixing: 0
\begin{aligned} \dot{m}_{1} t_{1}+\dot{m}_{2} t_{2} &=\dot{m}_{3} t_{3} \\ 1.645 \times 5+2.632 \times 34 &=4.277 t_{3} \\ t_{3} &=22.85^{\circ} \mathrm{C}\\ \text{Heat gain }:&=h_{4}-h_{3}\\ &=\dot{m}_{3} c_{p}\left(t_{4}-t_{3}\right) \\ &=4.277 \times 1.005(24-22.85) \\ &=4.963 \mathrm{~kW} \end{aligned}
 Question 6
The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapour equal to $p_v$. The saturation pressure of water at 300 K is $p_{sat}$. The correct relation for the air-water mixture is
 A $p_v=0.5p_{sat}$ B $p_v=p_{sat}$ C $p_v=0.622p_{sat}$ D $p_v=2p_{sat}$
GATE ME 2021 SET-1      Properties of Moist Air
Question 6 Explanation:
\begin{aligned} \text { Relative humidity, } \phi &=\frac{p_{v}}{p_{\text {sat }}} \\ 0.5 &=\frac{p_{v}}{p_{\text {sat }}} \\ p_{v} &=0.5 p_{\text {sat }} \end{aligned}
 Question 7
Superheated steam at 1500 kPa, has a specific volume of 2.75 $m^3$/kmol and compressibility factor ($Z$) of 0.95. The temperature of steam is $^{\circ}C$ (round off to the nearest integer).
 A 522 B 471 C 249 D 198
GATE ME 2021 SET-1      Heat Pumps and Cycles
Question 7 Explanation:
\begin{aligned} P &=1500 \mathrm{kPa} \\ V &=2.75 \mathrm{~m} 3 / \mathrm{k}-\mathrm{mol} \\ Z &=0.95 \\ P V &=n \bar{R} T \\ P \bar{V} &=\bar{R} T \\ P \bar{V} &=Z \times n \bar{R} T \\ P \frac{\bar{V}}{n} &=Z \bar{R} T \\ P_{\bar{V}} &=Z \bar{R} T\\ 1500 \mathrm{KPa} \times 2.75 \mathrm{~m}^{3} / \mathrm{K}-\mathrm{mol}&=0.95 \times 8.314 \mathrm{~kJ} / \mathrm{K}-\mathrm{molK} \times T\\ T&=522.26 \mathrm{~K}\\ T&=522.26-273=249.26^{\circ} \mathrm{C} \end{aligned}
 Question 8
Consider an ideal vapour compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle?
 A Coefficient of performance is higher than that of the original cycle. B Coefficient of performance is lower than that of the original cycle. C Coefficient of performance is the same as that of the original cycle. D Refrigerating effect is lower than that of the original cycle.
GATE ME 2019 SET-1      Vapor and Gas Refrigeration
Question 8 Explanation:
Due to isentropic expansion instead of throttling
1. R.E increases
2. Work input reduces
$\therefore \mathrm{COP}=\frac{\mathrm{R} \cdot \mathrm{E}}{\mathrm{W}_{\mathrm{in}}}$

 Question 9
Ambient air is at a pressure of 100 kPa, dry bulb temperature of $30^{\circ}C$ and and 60% relative humidity. The saturation pressure of water at $30^{\circ}C$ is 4.24 kPa. The specific humidity of air (in g/kg of dry air) is ________ (correct to two decimal places).
 A 102.25 B 8.68 C 18.68 D 16.24
GATE ME 2018 SET-2      Properties of Moist Air
Question 9 Explanation:
\begin{aligned} P_{\mathrm{atm}} &=100 \mathrm{kPa} \\ D B T &=t=30^{\circ} \mathrm{C} \rightarrow P_{v s}=4.24 \mathrm{kPa} \\ \phi &=60 \%\\ \phi &=\frac{P_{V}}{P_{V S}} \Rightarrow 0.6=\frac{P_{V}}{4.24} \\ P_{V} &=2.544 \mathrm{kPa} \\ W &=0.622 \times \frac{P_{V}}{P_{\mathrm{atm}}-P_{V}} \\ W &=0.622 \times \frac{2.544}{100-2.544} \\ W&=16.24 \text{gram/kg of dry Air} \end{aligned}
 Question 10
A standard vapor compression refrigeration cycle operating with a condensing temperature of $35^{\circ}C$ and an evaporating temperature of $-10^{\circ}C$ develops 15 kW of cooling. The p-h diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is 0.75, the magnitude of compressor power (in kW) is _________ (correct to two decimal places).
 A 8 B 10 C 12 D 6
GATE ME 2018 SET-2      Vapor and Gas Refrigeration
Question 10 Explanation:
\begin{aligned} R C &=15 \mathrm{kW} \\ R C &=\dot{m} \times\left(h_{1}-h_{4}\right) \\ 15 &=\dot{m} \times(400-250) \\ \dot{m} &=0.1 \mathrm{kg} / \mathrm{sec} \\ \omega_{\text {isentropic }} &=\left(h_{2}-h_{1}\right)=(475-400)=75 \mathrm{kJ} / \mathrm{kg}\\ \eta_{C} &=\frac{\omega_{\text {isentropic }}}{\omega_{\text {actual }}} \\ \omega_{\text {actual }} &=\frac{75}{0.75}=100 \mathrm{kJ} / \mathrm{kg} \\ \omega_{\text {actual }} &=\dot{m} \times \omega_{\text {actual }}=0.1 \times 100 \\ P_{\dot{m}} &=10 \mathrm{kW} \end{aligned}
There are 10 questions to complete.

### 3 thoughts on “Refrigeration and Air-conditioning”

1. ques 9 solution is wrong.. need to be checked…