$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively,then the ratio $\frac{T_2}{T_1}$ is:
- A$\left[\frac{L_1}{L_2}\right]^{2/3}$
- B$\left[\frac{L_1}{L_2}\right]^{1/2}$
- C$\left[\frac{L_2}{L_1}\right]^{1/2}$
- D$\left[\frac{L_2}{L_1}\right]^{2/3}$
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In which of the following complexes is the oxidation state of the metal zero?
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$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to a volume $\frac{V_i}{32}$,where $V_i$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$. The value of $x$ is:
Match the compounds in List$-I$ with the appropriate observations in List$-II$ and choose the correct option.
List$-I$
List$-II$
$(P)$ image
$(1)$ Reaction with phenyl diazonium salt gives yellow dye.
$(Q)$ image
$(2)$ Reaction with ninhydrin gives purple color and it also reacts with $FeCl _3$ to give violet color.
$(R)$ image
$(3)$ Reaction with glucose will give corresponding hydrazone.
$(S)$ image
$(4)$ Lassiagne extract of the compound treated with dilute HCl followed by addition of aqueous $FeCl _3$ gives blood red color.
$(5)$ After complete hydrolysis, it will give ninhydrin test and it $\text{DOES NOT}$ give positive phthalein dye test.
| List$-I$ | List$-II$ |
| $(P)$ image | $(1)$ Reaction with phenyl diazonium salt gives yellow dye. |
| $(Q)$ image | $(2)$ Reaction with ninhydrin gives purple color and it also reacts with $FeCl _3$ to give violet color. |
| $(R)$ image | $(3)$ Reaction with glucose will give corresponding hydrazone. |
| $(S)$ image | $(4)$ Lassiagne extract of the compound treated with dilute HCl followed by addition of aqueous $FeCl _3$ gives blood red color. |
| $(5)$ After complete hydrolysis, it will give ninhydrin test and it $\text{DOES NOT}$ give positive phthalein dye test. |
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