Question

gas occupies 200 ml at a pressure of 27 degree celsius and 76 mmhg pressure find volume at -3 degree celsius with pressure remaining constant

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Answer 1

$\huge{\underline{\underline {\mathtt{\purple{Hlw}\pink{mate}}}}}$

$\Large\bold\blue{Given:}$

Initial volume = 200ml

Initial temperature = 27°C

Final temperature = -3°C

$\Large\bold\blue{To Find :}$

Final volume of the gas.

$\Large\bold\blue{Solution :}$

Charles' law States that (V ∝ T)

$Formula : \underline{\boxed{\bf{\pink{\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}}}}}$

Let,

V₁ = Initial volume

V₂ = Final volume

T₁ = Initial temperature

T₂ = Final temperature

Convert unit of temperature from °C to K.

0°C = 273K

T₁ = 27°C = 27 + 273 = 300K

T₂ = -3°C = -3 + 273 = 270K

Substituting the given values,

V₁ / T₁ = V₂ / T₂

200 / 300 = V₂ / 270

V₂ = 270 × 2/3

$\Large\green{V₂\:=\:180 ml}$

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Answer 2

Question :-

  → Deduce the following equations of motion :-

             $s = ut \: + \frac{1}{2} at^{2}$

Solution :-

  → u = initial velocity

  → v = final velocity

  → t = time

  → s = distance

⇒ The distance travelled in time t =

   → Area of Trapezium OABD

   →  Area of rectangle OAED + Area of Triangle ΔABE

              or

   $s \: = \: \frac{1}{2} \times (OA + DB ) \times OD$

   $s = \frac{1}{2} \times (u +v) \times t$

⇒ Since , v = u + at

   

   $s = \frac{1}{2} \times ( u + u + at ) \times t$

    $s = ut + (\frac{1}{2})at^{2}$