An ideal monoatomic gas of volume V is adiaba | vedclass

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

Question

(A) For an adiabatic process, the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma-1} = 	ext{constant}$.Given, initial vo

Vedclass · Accepted Answer

$144.2$

Vedclass · Answer

(A) For an adiabatic process, the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma-1} = 	ext{constant}$.Given, initial volume $V_1 = V$, final volume $V_2 = 3V$, and initial temperature $T_1 = 27^{\circ}C = 27 + 273 = 300 	ext{ K}$.The adiabatic index $\gamma = \frac{C_P}{C_V} = \frac{5}{3}$.Using the relation $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$, we get:$\frac{T_2}{T_1} = \left(\frac{V_1}{V_2}ight)^{\gamma-1}$$\frac{T_2}{300} = \left(\frac{V}{3V}ight)^{\frac{5}{3}-1} = \left(\frac{1}{3}ight)^{\frac{2}{3}}$$T_2 = 300 	imes (3)^{-\frac{2}{3}} = 300 	imes \frac{1}{3^{0.666}} \approx 300 	imes 0.4807 \approx 144.2 	ext{ K}$.

An ideal monoatomic gas of volume $V$ is adiabatically expanded to a volume $3V$ at $27^{\circ}C$. The final temperature in Kelvins is (use $\frac{C_P}{C_V} = \frac{5}{3}$)

Similar Questions

For an adiabatic compression of $1 \text{ kmol}$ of gas,$146 \text{ kJ}$ of work is done. During this process,the temperature of the gas increases by $7 \text{ °C}$. The gas is ........

One mole of nitrogen gas being initially at a temperature of $T_0 = 300 \,K$ is adiabatically compressed to increase its pressure $10$ times. The final gas temperature after compression is (Assume, nitrogen gas molecules as rigid diatomic and $100^{1/7} = 1.9$) (in $\,K$)

$A$ motor tube is filled with air at $27^{\circ}C$ and a pressure of $8 \text{ atm}$. If the tube suddenly bursts,what will be the final temperature of the air? $(\gamma = 1.5)$

If during an adiabatic process the pressure of a mixture of gases is found to be proportional to the square of its absolute temperature,the ratio of $C_p / C_v$ for the mixture of gases is .........

The $P-V$ diagram for two adiabatic processes is given. Curves $1$ and $2$ correspond to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module