Question 683: Thermodynamics & KTG

Question

When an ideal gas $\left(\gamma=\frac{5}{3}\right)$ is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?

Accepted Answer

Step 1: Recall relation between Cv, Cp, and ÃÂ³
$ \gamma = \frac{C_p}{C_v}, \quad C_p - C_v = R $
Given:
$ \gamma = \frac{5}{3} $
Step 2: Express $C_v$ and $C_p$ in terms of R
$ \frac{C_p}{C_v} = \frac{5}{3} $
$ C_p = \frac{5}{3} C_v $
And:
$ C_p - C_v = R \implies \frac{5}{3}C_v - C_v = R \implies \frac{2}{3} C_v = R $
So:
$ C_v = 	frac{3}{2}R, \quad   C_p = 	frac{5}{2}R $
Step 3: Fraction of heat used for work in isobaric process
At constant pressure, if temperature rises by $\Delta T$:
Heat supplied:
$ Q = n C_p \Delta T $
Work done:
$ W = nR \Delta T $
Fraction used for work:
$ \frac{W}{Q} = \frac{nR \Delta T}{n C_p \Delta T} = \frac{R}{C_p} $
Step 4: Substitute values
$ \frac{W}{Q} = \frac{R}{	frac{5}{2}R} = \frac{2}{5} = 0.4 $
So:
$ 40\% $
Ã¢ÂÂ Final Answer:
Option D: $40 \%$

Answer

$60 \%$

Answer

$20 \%$

Answer

$30 \%$

Answer

$40 \%$

Thermodynamics & KTG

When an ideal gas \left(\gamma=\frac{5}{3}\right) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?

Choose the correct answer: