In an isobaric process of an ideal gas,the ra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For an isobaric process,the pressure $P$ remains constant.Heat supplied to the system is given by $Q = n C_{P} \Delta T$.Work done by the system i

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) For an isobaric process,the pressure $P$ remains constant.Heat supplied to the system is given by $Q = n C_{P} \Delta T$.Work done by the system is given by $W = P \Delta V$.Using the ideal gas equation $PV = nRT$,for a constant pressure process,$P \Delta V = nR \Delta T$.Therefore,$W = nR \Delta T$.The ratio of heat supplied to work done is $\frac{Q}{W} = \frac{n C_{P} \Delta T}{n R \Delta T} = \frac{C_{P}}{R}$.We know that $C_{P} - C_{V} = R$,so $R = C_{P} - C_{V}$.Substituting $R$ in the ratio: $\frac{Q}{W} = \frac{C_{P}}{C_{P} - C_{V}}$.Dividing the numerator and denominator by $C_{V}$: $\frac{Q}{W} = \frac{C_{P}/C_{V}}{(C_{P}/C_{V}) - 1}$.Since $\frac{C_{P}}{C_{V}} = \gamma$,we get $\frac{Q}{W} = \frac{\gamma}{\gamma - 1}$.

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

Similar Questions

$A$ diatomic gas $(\gamma = 1.4)$ does $400 \ J$ of work when it is expanded isobarically. The heat given to the gas in the process is ............ $J$.

In an isochoric process,if $t_1 = 27^{\circ}C$ and $t_2 = 127^{\circ}C$,then $\frac{P_1}{P_2}$ will be equal to [$P_1$ and $P_2$ are the pressures at $t_1^{\circ}C$ and $t_2^{\circ}C$ respectively].

$A$ diatomic gas with rigid molecules does $10 \ J$ of work when expanded at constant pressure. What would be the heat energy absorbed by the gas,in this process ..... $J$.

The ratio of specific heats of a gas is $\gamma$. The change in internal energy of one mole of the gas, when the volume changes from $V$ to $2V$ at constant pressure $p$, is:

When heat is given to a gas in an isobaric process,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module