In a flexible balloon, 2 moles of $S O_{2}$ having an initial volume of $1 k L$ at a temperature of $27^{o} C$ is filled. ( $S O_{2}$ is a linear triatomic gas). The gas is first expanded to thrice its initial volume isobarically and then expanded adiabatically so as to attain its initial temperature. Assuming gas is ideal and $R = \frac{25}{3} J m o l^{- 1} K^{- 1}$ change in internal energy of the gas in the isobaric process is:

3.5 \times 10^{4} J

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1.2 \times 10^{6} J

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3 \times 10^{5} J

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0.5 \times 10^{3} J

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Solution

The correct option is C $3.5 \times 10^{4} J$
In isobaric process the pressure remains constant.
Ideal gas equation: $P V = n R T$ $\Rightarrow \frac{V}{T} = \frac{n R}{P}$
$∴ \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ ;
Given:
$V_{1} = 1 k l = 1000 c c$
$T_{1} = 27^{o} C = (27 + 273) K = 300 K$
$∴ \frac{1000}{300} = \frac{3000}{T_{2}}$
$\Rightarrow T_{2} = 900^{0} K$
For the triatomic gas $S O_{2}$ , $γ = \frac{2 + f}{f} = \frac{2 + 7}{7} = \frac{9}{7}$ since there are three translational, two rotational degrees of freedom making it a total of 7 degrees of freedom.
For the adiabatic process, Change in internal energy
$d U = n C_{v} Δ T = n \frac{R}{γ - 1} Δ T$

$= \frac{7}{2} n R Δ T = \frac{7}{2} \times 2 \times R \times (900 - 300)$

$= \frac{7}{2} \times 2 \times \frac{25}{3} \times (900 - 300) = 3.5 \times 10^{4}$

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In a flexible balloon, 2 moles of $S O_{2}$ having initial volume of 1kl at a temperature of $27^{o} C$ is filled. ( $S O_{2}$ is a linear triatomic gas). The gas is first expanded to thrice its initial volume isobarically and then expanded adiabatically so as to attain its initial temperature. Assuming gas is ideal, $γ = \frac{4}{3}$ and $R = \frac{25}{3} J m o l^{- 1} K^{- 1}$ . Work done by the gas in the whole process is:

Q. In a flexible balloon,

2

moles of

S O_{2}

having initial volume of

1 k l

at a temperature of

27^{o} C

is filled (

S O_{2}

is a non linear triatomic gas). The gas is first expanded to thrice its initial volume isobarically and then expanded adiabatically so as to attain its initial temperature. Assuming gas is ideal and

R = \frac{25}{3} J m o l^{- 1} K^{- 1}

. Choose the incorrect options.

An ideal gas at 300 K occupies a volume of 0.5 $m^{3}$ at a pressure of 2 atm. The gas expands adiabatically until its volume is 1.2 $m^{3}$ . Next, the gas is compressed isobarically to its original volume. Finally, the pressure is increased isochorically until the gas returns to its initial state. Represent the change on the P-V diagram. Determine the temperature at the end of each transformation; and the work done during the cycle. Assume g = 1.4.