Question 716: Thermodynamics & KTG

Question

In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged $(\mathrm{Q})$ is $\left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)$

Accepted Answer

In an isobaric process for an ideal gas, we need to determine the ratio of the work done by the system (W) during expansion to the heat exchanged (Q). Here, $\gamma = \frac{C_p}{C_v}$ represents the ratio of specific heats.
For an isobaric process, the formulas are as follows:
Heat exchanged, $ Q = nC_p \Delta T $
Work done, $ W = n(C_p - C_v) \Delta T $
Now, let's find the ratio of work done to heat exchanged:
$ \begin{aligned} \frac{W}{Q} &= \frac{n(C_p - C_v) \Delta T}{nC_p \Delta T} \             &= \frac{C_p - C_v}{C_p} \             &= 1 - \frac{C_v}{C_p} \end{aligned} $
Given that $\gamma = \frac{C_p}{C_v}$, we can substitute this relationship into the equation:
$ 1 - \frac{C_v}{C_p} = 1 - \frac{1}{\gamma} = \frac{\gamma - 1}{\gamma} $
Thus, the ratio of work done to heat exchanged in an isobaric process is $\frac{\gamma - 1}{\gamma}$.

Answer

$\gamma$

Answer

$\gamma-1$

Answer

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

Answer

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

Thermodynamics & KTG

In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged (\mathrm{Q}) is \left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)

Choose the correct answer: