Question

A fixed mass of gas has a volume of 750cm3 at 23degree celsius and 800 mm pressure. Calculate the pressure for which its volume will be 720cm3, the temperature being -3degree celsius.

Answer 1

Question:

A fixed mass of gas has a volume of 750 cm³ at -23°C and 800 mm pressure. Calculate the pressure for which its volume will be 720 cm³, the temperature being -3° C.

Answer:

Final pressure of gas = 900 mm Hg

Explanation:

Given:

• Initial Volume of gas (V₁) = 750 cm³
• Initial Pressure of gas (P₁) = 800 mm Hg
• Initial Temperature of gas (T₁) = -23° C
• Final Volume of gas (V₂) = 720 cm³
• Final Temperature of gas (T₂) = -3° C

To Find:

• Final Pressure of gas (P₂)

Solution:

First convert all the given units to their standard units

Converting temperature from Celsius scale to Kelvin scale,

-23° C = 250.15 K

-3° C = 270.15 K

Now by the general gas equation we know that,

$\tt \dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}$

Substituting the data we get,

$\tt \dfrac{800\times 750}{250.15} =\dfrac{P_2\times 720}{270.15}$

Simplifying,

$\tt \dfrac{60000}{250.15} =\dfrac{P_2\times 72}{270.15}$

239.856 = P₂ × 0.2665

P₂ = 239.856/0.2665

P₂ = 900 mm Hg

Hence the final pressure of the gas would be 900 mm Hg.

Answer 2

$\Large{\pink{\underline{\textsf{\textbf{Question\::}}}}}$

A fixed mass of gas has a volume of 750 cm³ at -23°C and 800 mm pressure. Calculate the pressure for which its volume will be 720cm³, the temperature being -3°C.

$\\ \Large{\blue{\underline{\textsf{\textbf{Answer\::}}}}}$

Gɪᴠᴇɴ ;-

Case - 1 ;-

• Volume of a fixed mass of gas is 750 cm³ at -23°C.

$\longmapsto\:\:\bf{V_1\:=\:750\:cm^3\:}$

$\longmapsto\:\:\bf{T_1\:=\:-23°C\:=\:-23\:+\:273\:=\:250\:K}$

• Pressure is 800 mm.

$\longmapsto\:\:\bf{P_1\:=\:800\:mm\:}$

CASE - 2 ;-

$\longmapsto\:\:\bf{V_2\:=\:720\:cm^3\:}$

$\longmapsto\:\:\bf{T_2\:=\:-3°C\:=\:-3\:+\:273\:=\:270\:K}$

Tᴏ Fɪɴᴅ ;-

• The pressure (P₂) of the gas in case-2.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ ;-

$\bf\blue{We\:know \:that,}$

☆ According to equation of gas in terms of pressure (P), absolute temperature (T) & volume (V) is

$\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{\dfrac{P_1\:V_1}{T_1}\:=\:\dfrac{P_2\:V_2}{T_2}\:}}}}}}$

$:\implies\:\:\bf{\dfrac{800\times{750}}{250}\:=\:\dfrac{P_2\times{720}}{270}\:}$

$:\implies\:\:\bf{\dfrac{600000}{25}\:=\:\dfrac{720\:P_2}{27}\:}$

$:\implies\:\:\bf{24000\:=\:\dfrac{720\:P_2}{27}\:}$

$:\implies\:\:\bf{720\:P_2\:=\:24000\times{27}\:}$

$:\implies\:\:\bf{720\:P_2\:=\:648000\:}$

$:\implies\:\:\bf{P_2\:=\:\dfrac{648000}{720}\:}$

$:\implies\:\:\bf\purple{P_2\:=\:900\:mm}$

$\Large\bf\orange{Therefore,}$

The pressure of the gas in case-2 is 900 mm.