Question

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

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

Answer 1

The correct option is C $7:5:2$

From first law of thermodynamics,
$\Delta Q=\Delta U+\Delta W$
As the process is isobaric, we can modify it as
$\Delta Q=\Delta U+\mu R\Delta T$
[$\because W=P\Delta V=\mu R\Delta T$]

Gas is ideal and diatomic in nature.
Change in internal energy
$\Delta U=\mu C_V\Delta T=\frac{5}{2}\mu R\Delta T$ $[\because C_V=\frac{5}{2}R]$
$\Rightarrow \Delta U=\frac{5}{2}\Delta W.......\left(1\right)$

Thus, heat supplied at a constant pressure, can be written as
$\Delta Q=\mu C_P\Delta T$
$\Rightarrow \Delta Q=\frac{7}{2}\mu R\Delta T$
$[\because C_P=\frac{7}{2}R]$
$\Rightarrow \Delta Q=\frac{7}{2}\Delta W......\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$, we get
$\Delta Q:\Delta U:\Delta W=7:5:2$
Hence, option (c) is the correct answer.