This set of Thermodynamics Aptitude Test focuses on “Ideal Gas-3”.
1. The ratio of cp/cv is designated by the symbol ɣ.
Explanation: This ratio is of importance in ideal gas computations.
2. Which of the following relation is correct?
a) cv = R/(ɣ-1)
b) cp = ɣR/(ɣ-1)
c) ɣ = cp/cv
d) all of the mentioned
Explanation: Since ɣ=cp/cv and cp-cv=R.
3. Which of the following values of n are correct?
a) for isobaric process, n=0
b) for isothermal process, n=1
c) for isentropic process, n=ɣ
d) all of the mentioned
Explanation: For isobaric process, pressure=constant, for isothermal process, temperature=constant and for isentropic process, entropy=constant.
4. For a isometric or isochoric process, n=infinity.
5. A spherical helium balloon of 10m diameter is at 15°C and 100 kPa. How much helium does it contain?
a) 57.5 kg
b) 67.5 kg
c) 77.5 kg
d) 87.5 kg
Explanation: V = (4π/3)r^3 = (π/6)D^3 = 523.6 m^3
m(He) = ρV = PV/RT
=(100 × 523.6)/(2.0771 × 288) = 87.5 kg.
6. A rigid tank of 1 m^3 contains nitrogen gas at 600 kPa and 400 K. If 0.5 kg of gas flows out then what is the final pressure given the final temperature is 375 K?
a) 501.9 kPa
b) 503.9 kPa
c) 506.9 kPa
d) none of the mentioned
Explanation: m =(PV/RT) = (600 × 1)/(0.2968 × 400) = 5.054 kg
therefore m2 = m – 0.5 = 5.054 – 0.5 = 4.554 kg
P2 = (m2RT2)/V = (4.554 × 0.2968 × 375)/1 = 506.9 kPa.
7. A cylindrical gas tank 1 m long having inside diameter of 20 cm, is evacuated and filled with carbon dioxide gas at 25°C. What pressure should be the pressure if there is to be 1.2 kg of carbon dioxide?
a) 2052 kPa
b) 2152 kPa
c) 2252 kPa
d) 2352 kPa
Explanation: V = A × L = (π/4)[(0.2)^2] × 1 = 0.031416 m^3
P V = mRT
P = [1.2×0.1889×(273.15 + 25) K)]/(0.031416 m^3)
= 2152 kPa.
8. A hollow metal sphere having an inside diameter of 150-mm is weighed first when evacuated and then after being filled to 875 kPa with an unknown gas. If the difference in mass is 0.0025 kg, and the temperature is 25°C, find the gas.
Explanation: V = (π/6)(0.15)^3 = 0.001767 m^3
M = (mRT/PV) = (0.0025 × 8.3145 × 298.2)/(875 × 0.001767) = 4.009
this is the mass of helium gas.
9. An auto-mobile tire has air at −10°C and 190 kPa. After sometime, the temperature gets up to 10°C. Find the new pressure.
a) 210.4 kPa
b) 224.4 kPa
c) 200.4 kPa
d) 204.4 kPa
Explanation: Assume constant volume and that air is an ideal gas
P2 = P1 × T2/T1
= 190 ×(283.15/283.15)
= 204.4 kPa.
10. A piston cylinder contains air at 600 kPa, 290 K and a volume of 0.01m^3. A constant pressure process gives 54 kJ of work out. Find the final temperature of the air.
a) 2700 K
b) 2800 K
c) 2900 K
d) 3000 K
Explanation: W = ∫ P dV = PΔV
ΔV = W/P = 54/600 = 0.09 m^3
V2 = V1 + ΔV = 0.01 + 0.09 = 0.1 m^3
Assuming ideal gas, PV = mRT, then we have
T2 = P2V2/(mR) = (P2V2)*T1/(P1V1)= (V2/V1)*T1
= (0.1/0.01)*290 = 2900 K.
Sanfoundry Global Education & Learning Series – Thermodynamics.
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