Question

The volume of a gas to 0°C is 100cm', what will be the volume of the same gas at 546°C
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Answer 1

Given :

• Initial temperature ( T₁ ) of gas = 0° C
• Initial volume ( V₁ ) of gas = 100 cm³
• Final temperature ( T₂ ) of gas = 546°C

Note - We are not provided any information about pressure, so we will assume that pressure remains constant during whole process.

To find :

Final volume ( V₂ ) of gas

Solution :

Using Charles's law at constant pressure Volume of gas is directly proportional to its temperature in Kelvin scale. That is, V ∝ T.

This gives,

$\sf \: \dfrac{V_1}{V_2} = \dfrac{T_1}{T_2} \: \: \: equation \: 1$

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Now first of all we need to find Temperature in Kelvin scale

• T₁ = 0°C

➝ T₁ = 0 + 273 K

➝ T₁ = 273 K

• T₂ = 546°C

➝ T₂ = 546 + 273 K

➝ T₂ = 819 K

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Now , putting value in equation 1, we get;

$\sf \implies \: \: \dfrac{100 \: {cm}^{3} }{V_2} = \dfrac{273}{819} \\ \\ \sf \implies \: \: \dfrac{100 \: {cm}^{3} }{V_2} = \dfrac{273}{273 \times 3}$

$\sf \implies \: \: \dfrac{100 \: {cm}^{3} }{V_2} = \dfrac{1}{ 3}$

$\sf \implies \: \: 100 \: {cm}^{3} \times 3 \: = \: V_2$

$\sf \implies \: V_2 \: = \bold{300 \: {cm}^{3} }$

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ANSWER : 300 cm³