Question

One mole of an ideal gas is put through a series of changes as shown in the figure in which 1,2,3 mark the three stages of the system. Find the Pressure at the three stages.

• A. 1] - 1.107, 2] - 2.214, 3] - 1.107
• B. 1] - 1.113,2] - 2.226, 3] - 2.226
• C. 1] - 2.214,2] - 1.107, 3] - 2.214
• D. 1] - 1.107, 2] - 2.214, 3] - 2.214

Answer 1

Answer: (B)

At stage (1)

$V =22.4\, L =22.4 \times 10^{-3} \,m ^{3}$

$T =300\, K , n =1 \,mol$

$p=\frac{n R T}{V}=\frac{1 mol \times 8.314\, Pa \,m ^{3}\, mol ^{-1} \,K^{-1} \times 300 K }{22.4 \times 10^{-3} \,m ^{3}}$

$=1.113 \times 10^{5} \,Pa =1.113 \,bar$

At stage (2) temperature is doubled but volume is constant. Thus, $P \propto T ,=2.226$ bar

At stage $(3), T$ is $300 \,K$ and $V$ is $11.2 \,L$ and as in stage (1)

$p=\frac{n R T}{V}=2.226 \,bar$