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Standard X

Physics

Ideal Gas Equation

1.0 k-mol of ...

Question

1.0 k-mol of a sample of helium gas is put through the cycle of operations shown in figure. BC is an isothermal process and $P_{A} = 1.00 a t m, V_{A} = 22.4 m^{3}, P_{B} = 2.00 a t m .$ What are $T_{A}, T_{B} a n d V_{C}$ ?

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Solution

Given : $P_{A} = 1 a t m$ $V_{A} = 22.4 m^{3} = 22.4 \times 10^{3}$ L $P_{B} = 2 a t m$ $n = 1000$

Using ideal gas equation at A, $P_{A} V_{A} = n R T_{A}$
$∴$ $1 \times 22.4 \times 10^{3} = 1000 \times 0.0821 \times T_{A}$ $⟹ T_{A} = 273 K$

Process AB : $V_{A} = V_{B}$
$⟹$ $\frac{P_{A}}{P_{B}} = \frac{T_{A}}{T_{B}}$

$∴$ $\frac{1}{2} = \frac{273}{T_{B}}$ $⟹ T_{B} = 546 K$
As the process $B C$ is isothermal, thus $T_{C} = T_{B} = 546 K$

Process AC : Pressure is constant $⟹ \frac{V_{C}}{V_{A}} = \frac{T_{C}}{T_{A}}$
$∴$ $\frac{V_{C}}{22.4} = \frac{546}{273}$ $⟹ V_{C} = 44.8 m^{3}$

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1.0 k-mol of a sample of helium gas is put through the cycle of operations shown in figure. BC is an isothermal process and PA=1.00atm,VA=22.4m3,PB=2.00atm. What are TA,TBandVC ?

1.0 k-mol of a sample of helium gas is put through the cycle of operations shown in figure. BC is an isothermal process and $P_{A} = 1.00 a t m, V_{A} = 22.4 m^{3}, P_{B} = 2.00 a t m .$ What are $T_{A}, T_{B} a n d V_{C}$ ?