An ideal gas at initial temperature T_0 and i | vedclass

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

Question

(A) For an adiabatic process, the relation between temperature and volume is $T V^{\gamma-1} = 	ext{constant}$.Step $1$: Adiabatic expansion from $V_

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(A) For an adiabatic process, the relation between temperature and volume is $T V^{\gamma-1} = 	ext{constant}$.Step $1$: Adiabatic expansion from $V_0$ to $2 V_0$.$T_0 V_0^{\gamma-1} = T_1 (2 V_0)^{\gamma-1} \Rightarrow T_1 = T_0 \left(\frac{1}{2}ight)^{\gamma-1}$.Step $2$: Isothermal expansion from $2 V_0$ to $5 V_0$.Since the process is isothermal, the temperature remains constant at $T_1$.Step $3$: Adiabatic compression from $5 V_0$ to $V_f$ such that the final temperature is $T_0$.$T_1 (5 V_0)^{\gamma-1} = T_0 (V_f)^{\gamma-1}$.Substituting $T_1$ from Step $1$:$T_0 \left(\frac{1}{2}ight)^{\gamma-1} (5 V_0)^{\gamma-1} = T_0 (V_f)^{\gamma-1}$.$\left(\frac{5 V_0}{2}ight)^{\gamma-1} = (V_f)^{\gamma-1}$.$V_f = 2.5 V_0$.Comparing with $V_f = \alpha V_0$, we get $\alpha = 2.5$.

Process	Condition
$(I)$ Adiabatic	$(A) \Delta W = 0$
$(II)$ Isothermal	$(B) \Delta Q = 0$
$(III)$ Isochoric	$(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D) \Delta U = 0$

	$AB$	$BC$	$CA$
$\Delta W$	$40 \, J$		$30 \, J$
$\Delta U$		$50 \, J$
$\Delta Q$	$150 \, J$	$10 \, J$

Similar Questions

$10,000$ small balls,each of mass $1 \, g$,strike a surface of area $1 \, cm^2$ per second with a velocity of $100 \, m/s$ perpendicular to the surface. They rebound with the same velocity. What is the pressure exerted on the surface?

One mole of an ideal gas $\left( \frac{C_p}{C_v} = \gamma \right)$ is heated according to the law $P = \alpha V$,where $P$ is the pressure of the gas,$V$ is the volume,and $\alpha$ is a constant. What is the molar heat capacity of the gas in this process?

Helium gas undergoes a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in the figure. The efficiency of this cycle is nearly ....... $\%$ (Assume the gas to be an ideal gas).

Vedclass Test Series

Exam Paper Generator

Online Exam Module