Question

prove that the volume of a gas at 273C is twice its volume 273 k, at constant pressure​

Answer 1

At constant pressure volume is directly proportional to temperature .
e.g
V=kT
where k is proportionality constant.
here you take temperature only in Kelvin .
now,
when T =273 Celsius
T= 273 +273 =2. (273) Kelvin
V=2(273) k

when T = 273 Kelvin
V" =(273) k
now,
V=2V"
hence proved

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Answer 2

Charles' Law states that the volume of a gas at constant pressure is directly proportional to temperature.

$\longrightarrow\sf{V\propto T}$

Therefore,

$\longrightarrow\sf{\dfrac{V_1}{V_2}=\dfrac{T_1}{T_2}}$

Here,

$\longrightarrow\sf{T_1=273\ K}$

And,

$\longrightarrow\sf{T_2=273^oC}$

$\longrightarrow\sf{T_2=(273+273)\ K}$

$\longrightarrow\sf{T_2=546\ K}$

Let $\sf{V_1}$ and $\sf{V_2}$ be the volumes of the gas at temperatures $\sf{T_1}$ and $\sf{T_2}$ respectively, at constant pressure.

Then, by Charles' Law,

$\longrightarrow\sf{\dfrac{V_1}{V_2}=\dfrac{T_1}{T_2}}$

$\longrightarrow\sf{\dfrac{V_1}{V_2}=\dfrac{273\ K}{546\ K}}$

$\longrightarrow\sf{\dfrac{V_1}{V_2}=\dfrac{1}{2}}$

$\longrightarrow\underline{\underline{\sf{V_2=2V_1}}}$

∴ Volume of gas at 273°C is twice that at 273 K.

Hence the Proof!