Question

A certain quantity of heat energy is given to a diatomic ideal gas which expands at constant pressure. The fraction of the heat energy that is converted into work is

• A. $\frac{2}{5}$
• B. $\frac{2}{7}$
• C. $\frac{1}{5}$
• D. $\frac{5}{7}$

Answer 1

The correct option is D $\frac{5}{7}$

Supplied heat at constant pressure,

$\Delta Q=n{C}_P\Delta T$

Change in internal energy,

$\Delta U=n{C}_V\Delta T$

ratio, $\frac{\Delta U}{\Delta Q}=\frac{n{C}_V\Delta T}{n{C}_P\Delta T}=\frac{C_V}{C_P}$. . . . . . . . .(1)

For diatomic ideal gas,

$C_P=\frac{7R}{2},C_V=\frac{5R}{2}$

From equation (1), we get

$\frac{\Delta U}{\Delta Q}=\frac{5R/2}{7R/2}=\frac{5}{7}$

$(5/7{)}^{th}$ part of heat supplied is used to increase internal energy.