Question

Keeping the pressure fixed at what temperature the volume of a gas become double of the original volume at 0°C ?

Answer 1

Answer:-

Let the final Temperature (T2) be T and initial Volume(V1) be V.

Given:

Initial Temperature (T1) = 0° C = 273.15° K

and the final Volume is twice it's original.

→ Final Volume (V2) = 2(V) = 2V

We know that,

Charley's law of gases states that at constant pressure the Volume of a gas is directly proportional to it's temperature.

$\implies\sf \large{v \: \: \alpha \: \: \frac{1}{t} }$

→ VT = k (Constant)

$\sf\implies \large{\frac{V_1}{T_1} = \frac{V_2}{T_2}}$

→ V/T = 2V/273.15

On cross multiplication we get,

→ 273.15V = 2VT

→ (273.15V)/2V = T

→ 136.5 = T

→ T2 = 136.5° K

Hence, the volume becomes twice it's original at 136.5° K.

Answer 2

Answer:

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• Let the final Temperature (T2) be T and initial Volume(V1) be V.

$\green{ \underline{ \boxed{ \sf{Given:-}}}}$

• Initial Temperature (T1) = 0° C = 273.15° K

• and the final Volume is twice it's original.

• → Final Volume (V2) = 2(V) = 2V

$\green{ \underline{ \boxed{ \sf{we \: know\:that,}}}}$

Charley's law of gases states that at constant pressure the Volume of a gas is directly proportional to it's temperature.

$\implies\sf\large V \: \alpha \frac{1}{t}$

→ VT = k (Constant)

$\implies\sf\large \frac{ v_{1}}{ t_{1}} = \frac{ v_{2} }{t _{2} }$

→ V/T = 2V/273.15

On cross multiplication we get,

→ 273.15V = 2VT

→ (273.15V)/2V = T

→ 136.5 = T

→ T2 = 136.5° K

$\bf$Hence, the volume becomes twice it's original at 136.5° K.

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