Properties Of Matter Ques 11
- When the gas bubble is at a height $y$ from the bottom, its temperature is
(2008, 4M)
(a) $T_0\left(\frac{p_0+\rho_1 g H}{p_0+\rho_i g y}\right)^{2 / 5}$
(b) $T_0\left(\frac{p_0+\rho_I g(H-y)}{p_0+\rho_I g H}\right)^{2 / 5}$
(c) $T_0\left(\frac{p_0+\rho_1 g H}{p_0+\rho_l g y}\right)^{3 / 5}$
(d) $T_0\left(\frac{p_0+\rho_l g(H-y)}{p_0+\rho_l g H}\right)^{3 / 5}$
Show Answer
Answer:
Correct Answer: 11.( b )
Solution:
- As there is no exhange of heat. Therefore, process is adiabatic. Applying,
$ \begin{aligned} T p^{\frac{1-\gamma}{\gamma}} & =\text { constant } \Rightarrow T_2 p_2^{\frac{1-\gamma}{\gamma}}=T_1 p_1^{\frac{1-\gamma}{\gamma}} \\ T_2 & =T_1\left(\frac{p_1}{p_2}\right)^{\frac{1-\gamma}{\gamma}}=T_1\left(\frac{p_2}{p_1}\right)^{\frac{\gamma-1}{\gamma}} \end{aligned} $
Substituting the values, we have
$ \begin{aligned} T_2 & =T_0\left[\frac{p_0+\rho_I g(H-y)}{p_0+\rho_I g H}\right]^{\frac{5 / 3-1}{5 / 3}} \\ & =T_0\left[\frac{p_0+\rho_I g(H-y)}{p_0+\rho_I g H}\right]^{2 / 5} \end{aligned} $
$\therefore$ Correct option is (b).
BETA
