Home
Class 11
PHYSICS
Two moles of helium gas undergo a cyclic...

Two moles of helium gas undergo a cyclic process as shown in Fig. Assuming the gas to be ideal, calculate the following quantities in this process

(a) The net change in the heat energy
(b) The net work done
(c) The net change in internal energy

Text Solution

Verified by Experts

As we know in a process, the change in head ererngy of heat shpplied to the gas is equal to the net work done by the gas
Here, AB is isobaric process. Hence, work done during this process form A to B is
`W_(AB) = P (V_(2) - V_(1)) = nRT (T_(2) - T_(1))`
or `W_(AB) = 2 xx 8.314 xx (400 - 300) = 1662.8 J`
Work done during isothermal process form B to C is
`W_(BC) = nRT_(C ) 1n (V_(2) // V_(1)) = nRT+(C ) 1n (P_(1) // P_(2))`
`= 2xx 8.314 xx 400 xx 1n (2) = 2 xx 8.314 xx 400 xx 0.693`
`= 4601.2 J`
Work done during isobaric process from C to D
`W_(CD) = nR (T_(D) - T_(C )) = 2 xx 8.314 xx (300 - 400)`
`= - 1662.8 J`
Work done during isothermal process from D to A
`W_(DA) = nRT_(D) 1m (P_(D)//P_(A))`
`= nRT_(D ) 1n (2)`
`= - 2 xx 8.314 xx 300 x 0.693`
`= - 3437.7 J`
Net down done
`= W_(AB) + W_(BC) + W_(CD)+ W_(DA)`
` = 1662.8 + 4610.2n- 1662.5 = 3457.7 = 1152.5 J`
Now from the first law of thermodynamics
`Delta Q = DeltaU + Delta W`
Here, `Delta Q = Delta W = 1152.5 J`
`So the heat given to the system is 1152.5 J
As the gas returns to its original state, there is no change in internal energy.
Promotional Banner

Topper's Solved these Questions

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 2.1|20 Videos

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 2.2|28 Videos

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger|11 Videos

  • KINETIC THEORY OF GASES

    CENGAGE PHYSICS ENGLISH|Exercise Compression|2 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Single correct anwer type|14 Videos

Similar Questions

Explore conceptually related problems

Two moles of helium gas undergo a cyclic process as shown in Fig. 19.2.14. Assuming the gas to be ideal, calculate the following quantitites in this process (a) the net change in heat energy (b) the net work done (c) the net change in internal energy.

Two moles of Helium gas undergo a reversible cyclic process as shown in figure. Assuming gas to be ideal, what is the net work involved in the cyclic process ?

Two moles of Helium gas undergo a reversible cyclic process as shown in figure. Assuming gas to be ideal, what is the net work involved in the cyclic process ?

Two moles of Helium gas undergo a reversible cyclic process as shown in figure. Assuming gas to be ideal, what is the net work involved in the cyclic process ?

Two moles of a monatomic ideal gas undergo a cyclic process ABCDA as shown in figure. BCD is a semicircle. Find the efficiency of the cycle.

A sample of helium is undergoing a cyclic process ABCA as shown. In which of the following processes heat is a absorbed by the gas?

One mole of an ideal gas undergoes a cyclic process ABCDA as shown in the P-V diagram, The net work done in the process is (1 atm=10^(6) dyne cm^(-2))

An ideal gas undergoes cyclic process ABCDA as shown in given p-V diagram. The amount of work done by the gas is

One mole of an ideal mono-atomic gas is taken round cyclic process ABC as shown in figure below. Calculate work done

One mole of an ideal mono-atomic gas is taken round cyclic process ABC as shown in figure below. Calculate work done