Air is filled in a motor tube at 27^{circ}C a | vedclass

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

Question

(C) When the tube suddenly bursts,the process is adiabatic.For an adiabatic process,the relationship between temperature and pressure is given by: $\f

Vedclass · Accepted Answer

$150 K$

Vedclass · Answer

(C) When the tube suddenly bursts,the process is adiabatic.For an adiabatic process,the relationship between temperature and pressure is given by: $\frac{T_2}{T_1} = \left(\frac{P_2}{P_1}ight)^{\frac{\gamma - 1}{\gamma}}$.Here,the initial temperature $T_1 = 27^{\circ}C = 27 + 273 = 300 K$.The initial pressure $P_1 = 8 	ext{ atm}$.After the tube bursts,the final pressure $P_2 = 1 	ext{ atm}$ (atmospheric pressure).The adiabatic index $\gamma = 1.5$.Substituting the values: $\frac{T_2}{300} = \left(\frac{1}{8}ight)^{\frac{1.5 - 1}{1.5}} = \left(\frac{1}{8}ight)^{\frac{0.5}{1.5}} = \left(\frac{1}{8}ight)^{\frac{1}{3}}$.Since $8 = 2^3$,we have $\left(\frac{1}{8}ight)^{\frac{1}{3}} = \frac{1}{2}$.Therefore,$T_2 = 300 	imes \frac{1}{2} = 150 K$.

Air is filled in a motor tube at $27^{\circ}C$ and at a pressure of $8$ atmospheres. The tube suddenly bursts,then the temperature of the air is $[\text{Given } \gamma \text{ of air} = 1.5]$.

Similar Questions

$A$ monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one-eighth of its original volume. The final pressure at constant entropy will be $.....P$.

$A$ rigid diatomic gas $(\gamma = 7/5)$ is compressed adiabatically to volume $(V_i/32)$, where $V_i$ is the initial volume. The initial temperature of the gas is $T_i \text{ K}$ and the final temperature is $x T_i \text{ K}$. The value of $x$ is

For an adiabatic expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to

The adiabatic bulk modulus of a perfect gas at pressure $P$ is given by:

$A$ 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? $(\gamma = 1.5)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module