Question 679: Thermodynamics & KTG

Question

In an isobaric process of an ideal gas, the ratio of heat supplied and work done by the system $\left(\frac{\mathrm{Q}}{\mathrm{W}}\right)$ is $\left[\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma\right]$.

Accepted Answer

Step 1: Recall expressions
For an
isobaric process
:
Heat supplied:
$ Q = n C_p \Delta T $
Work done:
$ W = P \Delta V $
But also, for an ideal gas:
$ P \Delta V = nR \Delta T $
So:
$ W = nR \Delta T $
Step 2: Ratio
$ \frac{Q}{W} = \frac{nC_p \Delta T}{nR \Delta T} = \frac{C_p}{R} $
Step 3: Simplify in terms of $\gamma$
We know the relation:
$ C_p - C_v = R $
and
$ \gamma = \frac{C_p}{C_v} $
So:
$ \frac{C_p}{R} = \frac{C_p}{C_p - C_v} = \frac{\gamma C_v}{(\gamma C_v - C_v)}  = \frac{\gamma C_v}{(\gamma - 1) C_v} = \frac{\gamma}{\gamma - 1} $
Ã¢ÂÂ Final Answer:
$ \frac{Q}{W} = \frac{\gamma}{\gamma - 1} $
Correct option: (C) $	frac{\gamma}{\gamma - 1}$

Answer

1

Answer

$\gamma$

Answer

$\frac{\gamma}{\gamma-1}$

Answer

$\frac{\gamma-1}{\gamma}$

Thermodynamics & KTG

In an isobaric process of an ideal gas, the ratio of heat supplied and work done by the system \left(\frac{\mathrm{Q}}{\mathrm{W}}\right) is \left[\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma\right].

Choose the correct answer: