MHT CET · Physics · Thermodynamics
A vessel is filled with an ideal gas at a pressure of 10 atm and temperature \(27^{\circ} \mathrm{C} .\) Half of the mass is removed from the vessel and temperature of the remaining gas is increased to \(87^{\circ} \mathrm{C}\). Then the pressure of the gas in the vessel will be
- A 5 atm
- B \(6 \mathrm{~atm}\)
- C \(7 \mathrm{~atm}\)
- D 8 atm
Answer & Solution
Correct Answer
(B) \(6 \mathrm{~atm}\)
Step-by-step Solution
Detailed explanation
Ideal gas equation
\(\begin{array}{c}p V=n R T \\\frac{p V}{T}=n R=\frac{m}{M} R \\\frac{m}{M} R=\frac{10 \times V}{300} \\\frac{m}{2 M} R=\frac{p V}{360}\end{array}\)
\(\begin{aligned}\frac{p V}{360} &=\frac{1}{2} \frac{10 \mathrm{~V}}{300} \\p &=\frac{3600}{2 \times 300}=6 \mathrm{~atm}\end{aligned}\)
\(\begin{array}{c}p V=n R T \\\frac{p V}{T}=n R=\frac{m}{M} R \\\frac{m}{M} R=\frac{10 \times V}{300} \\\frac{m}{2 M} R=\frac{p V}{360}\end{array}\)
\(\begin{aligned}\frac{p V}{360} &=\frac{1}{2} \frac{10 \mathrm{~V}}{300} \\p &=\frac{3600}{2 \times 300}=6 \mathrm{~atm}\end{aligned}\)
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