## GATE ME solved Questions on Basics of Thermodynamics

**Question #1**

The internal energy of an ideal gas is a function of

(A) temperature and pressure

(B) volume and pressure

(C) entropy and pressure

(D) temperature only

**[GATE 16 S2, 1 mark]**

**Question #2**

Temperature of nitrogen in a vessel of volume 2 m^{3} is 288 K. A U-tube manometer connected to the vessel shows a reading of 70 cm of mercury (level higher in the end open to atmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325 bar, acceleration due to gravity is 9.81 m/s^{2} and density of mercury is 13600 kg/m^{3}. The mass of nitrogen (in kg) in the vessel is _____________

**[GATE 15 S1, 2 marks ]**

**Question #3**

A certain amount of an ideal gas is initially at a pressure p_{1} and temperature T_{1}. First, it undergoes a constant pressure process 1-2 such that T_{2} = 3T_{1}/4. Then, it undergoes a constant volume process 2-3 such that T_{3} = T_{1}/2. The ratio of the final volume to the initial volume of the ideal gas is _________

**[GATE 15 S1, 2 marks ]**

(A) 0.25

(B) 0.75

(C) 1.0

(D) 1.5

**Question #4**

The Van der Waals equation of state is $\left(p+\frac{a}{v^2} \right)(v-b)=RT$ where p is pressure, v is specific volume, T is temperature and R is characteristic gas constant. The SI unit of a is

(A) J/kg-K

(B) m^{3}/kg

(C) m^{5}/kg-s^{2}

(D) Pa/kg

*Common data Question*

A football was inflated to a gauge pressure of 1 bar when the ambient temperature was 15 ^{o} C.When the game started next day, the air temperature at the stadium was 5^{o}C. Assume that the volume of the football remains constant at 2500 cm^{3}.

**Question #5**

The amount of heat lost by the air in the football and the gauge pressure of air in the football at the stadium respectively equals

(A) 30.6 J, 1.94 bar

(B) 21.8 J, 0.93 bar

(C) 61.1 J, 1.94 bar

(D) 43.7 J, 0.93 bar

**[GATE 2006, 2 marks]**

**Question #6**

Gauge pressure of air to which the ball must have been originally inflated so that it would equal 1 bar gauge at the stadium is

(A) 2.23 bar

(B) 1.94 bar

(C) 1.07 bar

(D) 1.00 bar

**[GATE 2006, 2 marks]**

**Question #7**

Match items from group, I, II, III, IV and V

Group I |
Group II |

When added to the system | |

E Heat |
G Positive |

F Work |
H Negative |

Group III |
Group IV |
Group V |

Differential | Function | Phenomenon |

I Exact |
K Path |
M Transient |

J Inexact |
L Point |
N Boundary |

(A) F-G-J-K-M

E-G-I-K-N

(B) E-G-I-K-N

F-H-I-K-N

(C) F-H-J-L-N

E-H-I-M-L

(D) E-G-J-K-N

F-H-J-K-N

**[GATE 2006, 2 marks]**

**Ask your doubts in the comment section below**