Question

A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_i$ (in Kelvin) and the final temperature is $a{T}_i$, the value of a is

• A. 4
• B. 5
• C. 2
• D. 3

Answer 1

The correct option is A 4

For adiabatic process, we can write $T{V}^{\gamma -1}=$ constant
$\gamma =\frac{7}{5}$ for diatomic gases

$T_i{V}^{\frac{7}{5}-1}=$ k(constant) -------initial condition

$a{T}_i{V}^{\frac{7}{5}-1}=$ k(constant) ------final condition

$T{V}^{\frac{7}{5}-1}=aT(\frac{V}{32}{)}^{\frac{7}{5}-1}$
$\therefore a=4$