(2023, Theromdynamic Process, Paper-1, Q-1)

One mole of an ideal gas expands adiabatically from w an initial state (𝑇A, 𝑉0) to final state (𝑇f, 5𝑉0). Another mole of the same gas expands isothermally from a different initial state (𝑇B,𝑉0) to the same final state (𝑇f , 5𝑉0). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is 𝛾. What is the ratio 𝑇A/𝑇B?

## Solutions

(2023, Thermodynamics Process, Paper-1, Q-2)

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas (Y = 5/3) and one mole of an ideal diatomic gas (= 7/5). Here, Y is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of 66 Joule when heated at constant pressure. The change in its internal energy is ** __** Joule.

## Solution

(2023, Kinetic theory of gases, Paper-2, Q-3)

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is Un and the speed of sound in the gas is vn. At a fixed

temperature and pressure, which of the following is the correct option ?

## Solution

Questions 4 ( 2023, Paper-2, Thermodynamic processes)

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the ܲ-ܸ diagrams below. In cycle I, processes a, b, c and d are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes a’, b’, c’, and d’, are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is WI and that during cycle II is WII. The ratio WI/ WII is _______

## Solution

Answer 2

PARAGRAPH Based

A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure P and its temperature becomes T = 360 K. The hot air with density rises up a vertical chimney of diameter d = 0.1 m and height h = 9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density = 1.2 kg m–3, pressure P and temperature T = 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in and T inside the chimney and the furnace. Also ignore the viscous effects.

[Given: The acceleration due to gravity g = 10 m s–2

and pi = 3.14]

Question 5 (2023, Paper-2, Paragraph based)

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is ** _**_____ gm s−1

## Solution

49.61

Question 6 (2023, Paper-2, paragraph based)

When the chimney is closed using a cap at the top, a pressure difference P develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the

stoppage of air flow, are negligible then the value of dP is **__**___ N m−2

.

## Solution

20