An ideal gas having initial pressures P, volume V and temperature R is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2.Obtain the work done by the gas during the expansion as a function of initial pressure P and volume V.

Question

An ideal gas having initial pressures P, volume V and temperature R is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2.Obtain the work done by the gas during the expansion as a function of initial pressure P and volume V.

Filo · Accepted Answer

We know that the work done by the gas during adiabatic expansion is given by

w = \frac{1}{( γ - 1 )} (P V - P^{'} V^{'}) .... (1)

where pressure

P^{'}

after expansion is obtained from the relation

\frac{P ^{'} V ^{'}}{T ^{'}} = \frac{P V}{T}

or,

P^{'} = P \times \frac{V}{V ^{'}} \times \frac{T ^{'}}{T} = P \times \frac{V}{5.66 V} \times \frac{T /2}{T} = \frac{P}{11.32}

Putting

γ = 1.4, v^{'} = 5.66 V

and

P^{'} = \frac{P}{11.32}

in Eq. (1), we have

w = \frac{1}{( 1.4 - 1 )} (P V - \frac{P}{11.32} \times 5.66 V)

= \frac{1}{0.4} (P V - \frac{1}{2} P V) = 1.25 P V

.

Question Text	An ideal gas having initial pressures $P$ , volume $V$ and temperature $R$ is allowed to expand adiabatically until its volume becomes $5.66 V$ while its temperature falls to $T /2$ . Obtain the work done by the gas during the expansion as a function of initial pressure $P$ and volume $V$ .
Answer Type	Text solution:1
Upvotes	150

An ideal gas having initial pressures $P$ , volume $V$ and temperature $R$ is allowed to expand adiabatically until its volume becomes $5.66 V$ while its temperature falls to $T /2$ .
Obtain the work done by the gas during the expansion as a function of initial pressure $P$ and volume $V$ .

Text solutionVerified

Practice questions from similar books