# Basics of Thermodynamics | GATE MCQs (Solved)

## 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 m3 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/s2 and density of mercury is 13600 kg/m3. 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 p1 and temperature T1. First, it undergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constant volume process 2-3 such that T3 = T1/2. 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) m3/kg

(C) m5/kg-s2

(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 5oC. Assume that the volume of the football remains constant at 2500 cm3.

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]