A given mass of a gas is compressed isotherma | vedclass

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

Question

(B) For an isothermal process,the temperature of the gas remains constant,so the gas obeys Boyle's law: $P_1 V_1 = P_2 V_2$.Given that the pressure is

Vedclass · Accepted Answer

$1.41$

Vedclass · Answer

(B) For an isothermal process,the temperature of the gas remains constant,so the gas obeys Boyle's law: $P_1 V_1 = P_2 V_2$.Given that the pressure is doubled,$P_2 = 2 P_1$.Thus,$P_1 V_1 = (2 P_1) V_2$,which gives $\frac{V_1}{V_2} = 2$.Now,the gas expands adiabatically until its original volume is restored,so $V_3 = V_1$.The adiabatic process follows $P V^\gamma = 	ext{constant}$,so $P_2 V_2^\gamma = P_3 V_3^\gamma$.Given $P_3 = 0.75 P_1$ and $P_2 = 2 P_1$,we have:$(2 P_1) V_2^\gamma = (0.75 P_1) V_1^\gamma$.Dividing both sides by $P_1$,we get $2 V_2^\gamma = 0.75 V_1^\gamma$.$\left(\frac{V_1}{V_2}ight)^\gamma = \frac{2}{0.75} = \frac{2}{3/4} = \frac{8}{3}$.Since $\frac{V_1}{V_2} = 2$,we have $2^\gamma = \frac{8}{3} = 2.667$.Taking the logarithm on both sides: $\gamma \log 2 = \log 2.667$.$\gamma = \frac{\log 2.667}{\log 2} \approx \frac{0.426}{0.301} \approx 1.41$.

$A$ given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be $0.75$ of its initial pressure. The ratio of the specific heats of the gas is approximately :

Similar Questions

$A$ solution of urea (molar mass $60 \ g \ mol^{-1}$) boils at $100.18 \ ^oC$ at atmospheric pressure. If $K_f$ and $K_b$ for water are $1.86$ and $0.512 \ K \ kg \ mol^{-1}$ respectively,the above solution will freeze at ......... $^oC$.

In which of the following arrangements,the order is not correct according to the property indicated against it?

The conversion of $O$-acylated phenol to $C$-acylated phenol in the presence of $AlCl_3$ is an example of which type of organic reaction?

Which of the following is the correct order for basic strength?

$\int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x \, dx$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module