# Thermal Engineering Questions and Answers – Reciprocating Compressor – Set 2

This set of Thermal Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Reciprocating Compressor – Set 2”.

1. Which of the following is the effect of increase in clearance ratio “C” for the given pressure ratio on volumetric efficiency in case of reciprocating compressor?
a) Volumetric efficiency increases
b) Volumetric efficiency decreases
c) Volumetric efficiency may increase or decrease
d) Volumetric efficiency is independent of clearance ratio

Explanation: We know that the volumetric efficiency is given by ηvol = 1 – C$$\bigg[(\frac{p_2}{p_1} )^{\frac{1}{n}} – 1\bigg]$$. According to the formula, if C increases, then the value of $$\bigg[(\frac{p_2}{p_1} )^{\frac{1}{n}} – 1\bigg]$$ will increase, and thus ηvol decreases.

2. Which of the following is the effect of increase in pressure ratio “rp” for the given clearance ratio and inlet pressure “P1” on volumetric efficiency in case of reciprocating compressor?
a) Volumetric efficiency may increase or decrease
b) Volumetric efficiency decreases
c) Volumetric efficiency increases
d) Volumetric efficiency is independent of pressure ratio

Explanation: The formula of volumetric efficiency is given by ηvol = 1 – C$$\bigg[(\frac{p_2}{p_1} )^{\frac{1}{n}} – 1\bigg]$$. As “rp”, increases, which is the ratio of exit pressure to the inlet pressure, the value of C$$\bigg[(\frac{p_2}{p_1} )^{\frac{1}{n}} – 1\bigg]$$ increases, hence the volumetric efficiency decreases.

3. Which of the following is the condition under which the volumetric efficiency equals to 100% in case of reciprocating compressor?
a) P1 = P2
b) P1 < P2
c) P1 > P2
d) Independent of pressure values

Explanation: The volumetric efficiency is given by ηvol = 1 – C$$\bigg[(\frac{p_2}{p_1} )^{\frac{1}{n}} – 1\bigg]$$. When P1 is equal to P2, the ratio (P2/P1)1/n is equal to one, and ηvol is 100%. And, it implies that the actual volume flow rate is equal to the maximum possible volume flow rate.

4. Which of the following is not an assumption in Two-stage Compression with an intercooler?
a) The effect of clearance is neglected
b) There is no pressure drop in the intercooler
c) The compression in both the cylinders (i.e. L.P. and H.P.) is isothermal (i.e. PVn = Constant)
d) The suction and delivery of air takes place at constant pressure

Explanation: The compression process in both the cylinders (i.e. L.P. and H.P.) is polytropic (i.e. PVn = Constant). In order to achieve isothermal compression, the compression process should be very slow so that the temperature remains constant, which is not possible in actual practice.

5. Consider a two stage air compressor, with perfect intercooling, delivers air at a pressure of 40bar, the suction conditions being 1bar and 15°C. If both cylinders have the same stroke, then which of the following is the ratio of the cylinder diameters, for the efficiency of compression to be maximum? Assume the index of compression to be 1.2.
a) (D1/D2) = 1
b) (D1/D2) = 1.50
c) (D1/D2) = 1.80
d) (D1/D2) = 2.51

Explanation:
Given: P3 = 40bar; P1 = 1bar; T1 = 15°C = 15 + 273 = 288K; n = 1.2;
We know that for perfect intercooling, the intercooler pressure is given by,
P2 = $$\sqrt{P_1 P_3}$$
P2 = $$\sqrt{1 × 40}$$

P2 = 6.32bar
The ratio of cylinder diameters is given by,
(D1/D2) = (P2/P1)1/2
(D1/D2) = (6.32/1)1/2
(D1/D2) = 2.51
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6. Volumetric efficiency is the ratio of clearance volume to the swept volume.
a) True
b) False

Explanation: Volumetric efficiency is defined as the fraction of actual volume flow rate to the maximum possible volume-flow rate for given dimensions and temperature condition. And, it is given by ηvol = 1 – C$$\bigg[(\frac{p_2}{p_1} )^{\frac{1}{n}} – 1\bigg]$$.

7. Which of the following signifies the breathing capacity of the compressor?
a) Volume flow rate
b) Mass flow rate
c) Volumetric efficiency
d) Overall efficiency

Explanation: Volumetric efficiency relates the actual volume flow rate with the maximum possible volume-flow rate. Thus, greater the value of volumetric efficiency; more will be the breathing capacity or actual volume-flow rate.

8. In a reciprocating compressor isothermal efficiency is the ratio of actual work to the isothermal work.
a) True
b) False

Explanation: Isothermal efficiency of a compressor is the ratio of isothermal work required with respect to the actual work required for the compression. Actual work required is always greater than isothermal work, because isothermal line has lower slope than isentropic line.

9. A single acting reciprocating air compressor has cylinder diameter and stroke of 120mm and 270mm respectively. The compressor sucks air at 1bar and 17°C and delivers at 12bar while running at 100r.p.m. What is the mass of air delivered by the compressor per minute? The compression follows the law pv1.2 = C. Consider R as 287kJ/kg-k.
a) 0.0053kg/min
b) 0.00365kg/min
c) 0.365 kg/min
d) 1 kg/min

Explanation:
Given: D = 120mm = 0.12m; L = 270mm = 0.27m;
P1 = 1bar = 1 × 105 N/m2; T1 = 17°C = 17 + 273 = 290K
P2 = 12bar = 12 × 105 N/m2; N = 100rpm; n = 1.2; R = 287kJ/kg-K
We know that volume of air before compression is,
V1 = $$\frac{\pi}{4}$$ × D2 × L,
V1 = $$\frac{\pi}{4}$$ × (0.12)2 × 0.27
V1 = 0.00305m3
Let m = mass of air delivered by the compressor per stroke.
We know that P1 V1 = mRT1
∴ m = $$\frac{P_1 V_1}{RT_1}$$

m = $$\frac{1 × 10^5 × 0.00305}{290 × 288}$$
m = 0.00365kg per stroke,
and mass delivered per minute = m × N = 0.00365 × 100 = 0.365kg/min.

10. A single acting reciprocating air compressor has cylinder diameter and stroke of 140mm and 320mm respectively. The compressor sucks air at 1bar and 27°C and delivers at 5bar while running at 100r.p.m. What is the temperature of air delivered by the compressor? The compression follows the law pv1.2 = C. Consider R as 287kJ/kg-k.
a) 119.25°C
b) 288°C
c) 134.29°C
d) 407.29°C

Explanation:
Given: D = 140mm = 0.14m; L = 320mm = 0.32m;
P1 = 1bar = 1 × 105 N/m2; T1 = 27°C = 27 + 273 = 300K
P2 = 5bar = 5 × 105 N/m2; N = 100rpm; n = 1.2 R = 287kJ/kg-K
Let T2 = Temperature of air delivered by the compressor,
We know that,
$$\frac{T_2}{T_1} = (\frac{P_2}{P_1})^{\frac{n-1}{n}}$$
$$\frac{T_2}{T_1} = (\frac{5}{1})^{\frac{1.2-1}{1.2}}$$
$$\frac{T_2}{T_1}$$ = 1.307
∴ T2 = 1.307 × T1
T2 = 1.307 × 300
T2 = 392.25K = 119.25°C.

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