5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T1, the work done in the process is

Engineering

Physics

Degree of Freedom Internal Energy of Gas and Specific Heat Capacity of Gases

Thermodynamics

Cyclic Processes

Question

5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T₁, the work done in the process is

$\frac{9}{8} {RT}_{1}$

$\frac{15}{8} {RT}_{1}$

$\frac{3}{2} {RT}_{1}$

$\frac{9}{2} {RT}_{1}$

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$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$

$T_{2} = T_{1} {(\frac{V_{1}}{V_{2}})}^{γ - 1}$

$= T_{1} {(\frac{5 .7}{0 .7})}^{\frac{5}{3} - 1} = T_{1} {(8)}^{2 / 3} = 4 T_{1}$

no. of mole = ¼

$W = \frac{nR (T_{1} - T_{2})}{γ - 1} = \frac{\frac{1}{4} \times R (4 T_{1} - T_{1})}{2 / 3} = \frac{9}{8} {RT}_{1}$