Question

An ideal diatomic gas is expanded so that the amount of heat transferred to the gas is equal to the decrease in its internal energy. The process can be represented by the equation $T{V}^n$= constant, where the value of n is

• A. n = 7/5
• B. n=1/5
• C. n=3/2
• D. n=3/5

Answer 1

Answer: (B)

. n=1/5

We have from I law of thermodynamics,

dQ = dU + dW
dQ = dU + P dV ____ (1)
But according to the problem
dQ = – dU ____ (2)
From (1) and (2)
-2 dU = P dV
Using dU = $n_{C_V}dT$ and PV = nRT we have
$-2n{C}_{V}dT=\frac{nRT}{V}dV$

( $C_v=\frac{5}{2}R$ for distomic gas)

$-5\frac{dT}{T}=\frac{dV}{V}$
On integrating
– 5 ln (T) = ln (V) + (K) (K: constant)
Or ln ($V{T}^5)$ = K
$\Rightarrow V{T}^5=RorT{V}^{(}\frac{1}{5})=k^{\prime }$
$\therefore n=\frac{1}{5}$