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Standard XII

Physics

Work

The pressure ...

Question

The pressure $p$ , volume $V$ and temperature $T$ for a certain gas are related by $p = \frac{A T - B T^{2}}{V}$ , where $A$ and $B$ are constants. the work done by the gas when the temperature changes from $T_{1}$ to $T_{2}$ while the pressure remains constant, is given by:

A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2})

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\frac{A (T_{2} - T_{1})}{V_{2} - V_{1}} - \frac{B (T_{2}^{2} - T_{1}^{2})}{V_{2} - V_{1}}

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A (T_{2} - T_{1}) - \frac{B}{2} (T_{2}^{2} - T_{1}^{2})

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\frac{A (T_{2} - T_{1}^{2})}{V_{2} - V_{1}}

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Solution

The correct option is C $A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2})$
Given, $P = \frac{A T - B T^{2}}{V}$
$\Rightarrow P V = A T - B T^{2}$
$\Rightarrow P Δ V = A Δ T - 2 B T Δ T$
On integrating, we get
Work $= \int P d V = A \int_{T_{1}}^{T_{2}} d T - 2 B \int_{T_{1}}^{T_{2}} T d T$
$= A (T_{2} - T_{1}) - B [(T_{2})^{2} - (T_{1})^{2}]$

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The pressure p, volume V and temperature T for a certain gas are related by p=AT−BT2V, where A and B are constants. the work done by the gas when the temperature changes from T1 to T2 while the pressure remains constant, is given by:

The correct option is C A(T2−T1)−B(T22−T21)Given, P=AT−BT2V⇒PV=AT−BT2⇒PΔV=AΔT−2BTΔTOn integrating, we getWork =∫PdV=A∫T2T1dT−2B∫T2T1TdT=A(T2−T1)−B[(T2)2−(T1)2]

The pressure $p$ , volume $V$ and temperature $T$ for a certain gas are related by $p = \frac{A T - B T^{2}}{V}$ , where $A$ and $B$ are constants. the work done by the gas when the temperature changes from $T_{1}$ to $T_{2}$ while the pressure remains constant, is given by: