Question

Heat is supplied to a diatomic gas at constant pressure. The ratio of $Q:\Delta U:W$is

• A.
  $5:3:2$
• B.
  $7:2:5$
• C.
  $5:2:3$
• D.
  $7:5:2$

Answer 1

The correct option is D

$7:5:2$
For diatomic gas,
$C_P=\frac{7}{2}R$
$C_V=\frac{5}{2}R$
$Q=\mu C_P\Delta T=\frac{7}{2}\mu R\Delta T\dots \left(i\right)$
$Q=\mu C_P\Delta T=\frac{5}{2}\mu R\Delta T\dots \left(ii\right)$
From $1^{st}$ law of thermodynamics,
$W=Q-\Delta U=\mu R\Delta T\dots \left(iii\right)$
From equation $\left(i\right)$, $\left(ii\right)$ and $\left(iii\right)$
$\Rightarrow Q:\Delta U:W=7:5:2$