Two thermally insulated vessels are filled with equal number of moles of air and connected by short tube with a value. If P, V and T and pressure, volume and temperature of gas in first vessel and 2P, V and T / 2 be pressure, volume and temperature of gas second vessel then find temperature and pressure of air after opening the value.

Solution

Calculate the heat absorbed by the system in going through one cycle for the cyclic process

shown in the Figure

Solution

when water is boiled under a pressure of 2 atm, the heat of vaporization is $2.20 \times 10^6$ J Kg

(a) Compute the work done when 1 kg of steam is formed at this temperature

(b) Compute the increase in internal energy

Solution

Figure below shows different paths. connecting state i to state f in P-V diagram along which gas can be taken Rank paths according to

(a) Change in internal energy

(b) Work done by gas

(c) The magnitude of energy transferred as heat.

Solution

Two moles of helium (γ=5/3) are initially at a temperature of 27 °C and occupy a volume of 20L. The helium is first expanded at constant pressure until the volume has tripled, and then adiabatically until the temperature returns to its initial state. given for helium

C

(a) Draw diagram of process in P-V plane

(b) What is the total heat supplied in the process

(c) What is the total change in internal energy of helium.

(d) What is the total work done by the helium.

(e) What is the final volume and pressure.

Solution

Temperature of a system containing 1 mole ideal gas increases by on amount ΔT = 30 K as a result of heating at constant pressure. If gas obtains an amount of heat Q= 3.2 KJ. then calculate

(a) work done by the gas

(b) change in its internal energy

(c) value of γ= C

Solution

Two moles of a certain ideal gas at a temperature T

(a) What would be total change in internal energy.

(b) Total work done by the system.

(c) Find the total amount of heat absorbed by gas in this process

Solution

An ideal gas where adiabatic exponent is equal to γ, is expanded so that the amount of heat transferred to the gas is equal to the decrease of internal energy find

(a) molor heat capacity of gas in this process

(b) equation of process in variables T, V

(c) Work performed by one mole of gas when its volume increases by η time if T

Solution

An ideal gas is taken from an initial state i to a final state f in such a way that the ratio of the pressure to the absolute temperature remains constant. What will be the work done by the gas.

Solution

Consider the cyclic process ABCA, shown in the Figure, performed on a sample of 2.0 mole of an ideal gas. A total of 1200 J of heat is withdrawn from the sample as the process. Find the work done by the gas during the part BC.

Solution

Consider a cylindrical tube of volume V with adiabatic walls containing an ideal gas. The internal energy of this ideal gas is given by 1.5 μRT. The tube is divided into two equal parts by a fixed diathenic wall. Initially, the pressure and the temperature are P

(a) How much work has been done on the left part.

(b) Find the final temperature on the two sides.

(c) Find the final pressure on the two sides.

Solution

1 moles of an ideal gas whose adiabatic exponent equals y undergoes a process in which gas pressure relates to the temperature as

P=aT

If the temperature get an increment of ΔT,find following

a. Change in Internal energy

b. Work performed by the gas

c. Molar heat capacity of the gas in the process

d. find the amount heat supplied

Solution

Two vessels A & B of equal volumes V

a. Find the temperature and pressure in the two vessels.

b The valve is now open for sufficient time so that gases acquire a common temperature and pressure. Find the new values of pressure and temperature

Solution

1 mole of an ideal gas whose adiabatic exponents is γ is enclosed in the vertical adiabatic vessel fitted with moving frictionless piston whose weight is W and cross-sectional area is A.The atmospheric pressure is P

a. Find the initial and final state of the gas

b. Find the work done by the gas

C. Find the change in internal energy

Solution

Two samples A and B whose adiabatic exponents is γ are initially kept in the same state (P

a. Find the ratio of the final pressure of the two samples

b. Find the ratio of the final temperature of the two samples

c. Find the ratio of the work done by the two samples

Solution

One mole of an ideal monatomic gas is taken round the cyclic process ABCDA as shown in figure.

a. Work done by the gas

b Heat absorbed by the gas in AB and BC

c. Heat in process CD

d. Find the temperature at C and D

e. Maximum temperature attained by the gas during the cycle

f. Net change in the internal energy and the heat

Solution

An ice cube of mass .1kg at 0 °C is placed in an isolated container which is at 227° C. The specific heat of the container varies with temperature according to the empirical formula

S=A + BT

where A is 100cal/kg-K and B is 2x10

if the final temperature of the container is 27°C.Determine the mass of the container.

Specific heat of water is 10

Latent heat of fusion of water is 8x10

Solution

A gaseous mixture is such that

Gas |
No of moles |
Adiabatic coefficient |

A |
1 |
1.67 |

B |
2 |
1.4 |

The gaseous mixture is taken through an adiabatic process where temperature of the mixture drops by ΔT.

a. Find the work done by the mixture

b. If m

Solution

A diatomic gas whose adiabatic coefficient is γ=1.4 is taken through XYZAX cycle.

X->Y Adiabatic compression

Y->Z Isobaric expansion

Z->A Adiabatic expansion

A->X Isochoric process

find the following

- Molar heat capacities in each process
- if the volume ratio is V
_{X}/V_{Y}=16 and V_{Z}/V_{Y}=2 and T_{Y}=636° C

b. find the net work done by the gas in the cycle

c. find the ratio of pressure P

Solution

Consider one mole of perfect gas in a cylinder of unit cross section with a piston attached in below figure. A spring (spring constant k) is attached (unstrectched length L ) to the piston and to the bottom of the cylinder. Initially the spring is unstrectched and the gas is in equilibrium. A certain amount of heat Q is supplied to the gas causing an increase of volume from $V_0$ to $V_1$.

(a) What is the initial pressure of the system?

(b) What is the final pressure of the system?

(c) Using the first law of thermodynamics, write down a relation between Q, $P_a$, V, $V_0$ and k.

Solution

- Introduction
- Concept of Heat
- P-V Indicator Digram
- |
- Work done by Gas in volume changes
- |
- Internal Energy
- |
- First Law of Thermodynamics
- |
- Specific Heat Capacity of Ideal GAS
- |
- Thermodynamic Processes
- |
- Quasi static Processes
- |
- Isothermal Process
- |
- Adiabatic Process
- |
- Isochoric process
- |
- Isobaric process
- |
- Cyclic process
- |
- Work done in Isothermal process
- |
- Work done in an Adiabatic process
- |
- Heat Engine and efficiency
- |
- Principle of a Refrigerator
- |
- Second law of thermodynamics
- |
- Reversibility and irreversibility
- |
- Carnot's Heat Engine
- |
- Carnot Theorem
- |
- Solved Examples

- Thermodynamics Questions
- |
- Multiple Choice Questions
- |
- P-V diagram Problems and Solutions
- |
- Carnot Cycle Problems

Class 11 Maths Class 11 Physics Class 11 Chemistry

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