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laws

Question

An ideal gas initially at pressure 1 bar is being compressed from 30 m³ to 10 m³ volume and its temperature decreases from 320 K to 280 K, then find the value of final pressure of the gas. [AIIMS 2019]

Easy

A

2.625 bar
B

3.4 bar
C

1.325 bar
D

4.5 bar

Solution

Given, initial pressure of ideal gas,
p₁ = 1 bar = $1 {NM}^{- 2}$
Initital volume, V₁ = 30 m³
Final volume, V_² = 10 m³
Initial temperature, T₁ = 320 K
Final temperature, T₂ = 280 K
Final pressure of gas, p₂ = ?
From ideal gas equation,
$\frac{p_{1} V_{1}}{T_{1}} = \frac{p_{2} V_{2}}{T_{2}}$
$\Rightarrow$ $\frac{1 \times 30}{320} = \frac{p_{2} \times 10}{280}$
$\Rightarrow$ p₂ = 2.625 bar

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