Question

An ideal gas with adiabatic exponent $\gamma$ is heated at constant pressure. It absorb Q amount of heat. Determine the fractions of heat absorbed in raising the internal energy and performing the work.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

At constant pressure heat absorbed by the system is,
$Q=n{C}_P\Delta T$
and internal energy change is,
$\Delta U=n{C}_V\Delta T$
Therefore the fraction,
$\frac{\Delta U}{Q}=\frac{n{C}_V\Delta T}{n{C}_P\Delta T}=\frac{C_V}{C_P}=\frac{1}{\gamma }$
From the first law of thermodynamics, we know
W = Q - DU
Therefore, the fraction,
$\frac{W}{Q}=\frac{Q-\Delta U}{Q}=1-\frac{\Delta U}{Q}=1-\frac{1}{\gamma }$
Note : In terms of the degree of freedom f, the above fractions may be written as
$\frac{\Delta U}{Q}=\frac{f}{f+2}$
and $\frac{W}{Q}=\frac{2}{f+2}$