A tyre filled with air (27^circ C and 2 text{ | vedclass

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

Question

(A) When a tyre bursts,the air undergoes an adiabatic expansion. The relationship between temperature and pressure for an adiabatic process is given b

Vedclass · Accepted Answer

$-33$

Vedclass · Answer

(A) When a tyre bursts,the air undergoes an adiabatic expansion. The relationship between temperature and pressure for an adiabatic process is given by: $\frac{T_2}{T_1} = \left( \frac{P_2}{P_1} ight)^{\frac{\gamma - 1}{\gamma}}$.Given: $T_1 = 27^\circ C = 300 	ext{ K}$,$P_1 = 2 	ext{ atm}$,$P_2 = 1 	ext{ atm}$ (atmospheric pressure),and $\gamma = 1.5$.Substituting the values: $\frac{T_2}{300} = \left( \frac{1}{2} ight)^{\frac{1.5 - 1}{1.5}} = \left( \frac{1}{2} ight)^{\frac{0.5}{1.5}} = \left( \frac{1}{2} ight)^{\frac{1}{3}}$.Since $2^{1/3} \approx 1.26$,we have $\frac{T_2}{300} = \frac{1}{1.26} \approx 0.793$.$T_2 = 300 	imes 0.793 \approx 238 	ext{ K}$.Converting to Celsius: $T_2(^\circ C) = 238 - 273 = -35^\circ C$. The closest option is $-33^\circ C$.

$A$ tyre filled with air ($27^\circ C$ and $2 \text{ atm}$) bursts. What is the final temperature of the air in $^\circ C$? (Given: $\gamma = 1.5$)

Similar Questions

$A$ gas at $37^{\circ} C$ is compressed adiabatically to half of its volume. What is the final temperature of the gas (in $^{\circ} C$)? (Ratio of specific heat capacities of the gas is $1.5$)

An ideal gas undergoes an adiabatic process. If the pressure of the gas is reduced by $0.1 \%$, then the volume is changed by (Given $\gamma = \frac{C_p}{C_v} = \frac{5}{3}$) (in $\%$)

The internal energy of the gas increases in:

At $N.T.P.$,one mole of a diatomic gas is compressed adiabatically to half of its volume. Given $\gamma = 1.41$,the work done on the gas will be approximately ....... $J$.

The process in which no heat enters or leaves the system is termed as

Vedclass Test Series

Exam Paper Generator

Online Exam Module