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Standard XII

Chemistry

Work Done in Reversible Adiabatic Process

For a thermod...

Question

For a thermodynamic system, the pressure, volume and temperature are related as $p = \frac{α T^{2}}{V}$ , where $α$ is a positive constant. The work done for this system in a constant pressure process, if the temperature changes from $T_{0}$ to $2 T_{0}$ is

$2 α T_{0}^{2}$

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$3 α T_{0}^{2}$

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$4 α T_{0}^{2}$

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None

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Solution

The correct option is B
$3 α T_{0}^{2}$

$P^{V} = α T^{2}$

$p d V + V d P = 2 α T d T$

For constant pressure process, $d P = 0 S$

$W = \int p d V = \int_{T_{0}}^{2 T_{0}} 2 α T d T$

$So p d V = 2 α T d T,$

$= 3 α T_{0}^{2}$

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For a thermodynamic system, the pressure, volume and temperature are related as p=αT2V, where α is a positive constant. The work done for this system in a constant pressure process, if the temperature changes from T0 to 2T0 is

The correct option is B 3αT20 PV=αT2 pdV+VdP=2αTdT For constant pressure process, dP=0 S W=∫pdV=∫2T0T02αTdT So pdV=2αTdT, =3αT20

For a thermodynamic system, the pressure, volume and temperature are related as $p = \frac{α T^{2}}{V}$ , where $α$ is a positive constant. The work done for this system in a constant pressure process, if the temperature changes from $T_{0}$ to $2 T_{0}$ is

The correct option is B
$3 α T_{0}^{2}$

$P^{V} = α T^{2}$

$p d V + V d P = 2 α T d T$

For constant pressure process, $d P = 0 S$

$W = \int p d V = \int_{T_{0}}^{2 T_{0}} 2 α T d T$

$So p d V = 2 α T d T,$

$= 3 α T_{0}^{2}$