Question

A diatomic gas does $80J$ of work when expanded isobarically. The heat given to the gas during this process is

• A. $700J$
• B. $350J$
• C. $280J$
• D. $300J$

Answer 1

The correct option is C $280J$

it is given that $W=80J$

from ideal gas equation

$P\Delta V=nR\Delta T$

$\because W=P\Delta T$

$\Delta T=\frac{80}{nR}..........\left(1\right)$

Change in internal energy is given by the relation as follows

$\Delta U=n{c}_v\Delta T$

$=n\frac{R}{\gamma -1}\Delta T..........\left(2\right)$

Here, diatomic gas is given so $\gamma =\frac{7}{5}$

Equation (2) becomes

$\Delta U=\frac{nR}{\frac{2}{5}}\Delta T$

$=\frac{5nR}{2}\times \frac{80}{nR}$

$=200J$

The heat given to the gas during this process is

$\Delta Q=\Delta U+W$

$\Delta Q=200+80$

$\Delta Q=280J$