Home
Class 11
PHYSICS
The value of gamma = C(P)//C(V) is 4//3 ...

The value of `gamma = C_(P)//C_(V)` is `4//3` for an adaibatic process of an ideal gas for which internal energy `U = K + nPV`. Find the value of `n` (`K` is constant) :

Text Solution

Verified by Experts

The correct Answer is:
3
`PV^(gamma) =` constant
`PV^(4//3) =` constant
In `(V^(4)) + I n (P^(3)) =` constant
`4 ((dV)/(V)) = - 3 ((dP)/(P))`
`4 P (dV) + 3 V (dP) = 0`
`3 (PdV + VdP) + PdV = 0`
For adiabatic process, `dQ = 0 = dU + dW`
`dU + PdV`
Compare Eps. (i) (ii), `dU = 3 (PdV + VdP)`
`U = K + 3PV`
So, `n = 3`
Promotional Banner

Topper's Solved these Questions

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS|Exercise Comprehension|56 Videos

  • KINETIC THEORY OF GASES

    CENGAGE PHYSICS|Exercise Compression|2 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS|Exercise Multiple Correct Answer Type|9 Videos

Similar Questions

Explore conceptually related problems

The value of gamma = C_(P)//C_(v) is 4//3 for an adiabatic process of an ideal gas for which internal energy U = A + BPV . The value of B will be (A is a constant)

P-V graph for an ideal gas undergoing polytropic process PV^(m) = constant is shown here. Find the value of m.

In previous, Find the value of gamma = C_(P) // C_(v) :

The internal energy of an ideal gas is sum of total kinetic energy of molecules. Consider an ideal gas in which the relation among U, P and V is U=2+3 PV The gas is

The relation between internal energy U , pressure P and volume V of a gas in an adiabatic process is U = a + bPV where a and b are constant . What is the effective value of adiabatic constant Y.

For an ideal gas the ratio of specific heats is (C_(p))/(C_(v)) = gamma . The gas undergoes a polytropic process PV^(n) = a constant. Find the values of n for which the temperature of the gas increases when it rejects heat to the surrounding.

The relation between U, p and V for an ideal gas in an adiabatic process is given by relation U=a+bpV . Find the value of adiabatic exponent (gamma) of this gas.

An ideal gas (C_p / C_v = gamma) is taken through a process in which the pressure and volume vary as (p = aV^(b) . Find the value of b for which the specific heat capacity in the process is zero.

An ideal gas with adiabatic exponent gamma = 4/3 undergoes a process in which internal energy is related to volume as U = V^2 . Then molar heat capacity of the gas for the process is :

An ideal gas with adiabatic exponent ( gamma=1.5 ) undergoes a process in which work done by the gas is same as increase in internal energy of the gas. Here R is gas constant. The molar heat capacity C of gas for the process is: