In an adiabatic process- 4 g of H2 gas expands and temperature changes from 47-C to 27-C- Find the magnitude of the work done by the gas on the surrounding-

For an adiabatic process, Δ Q = Δ W + Δ U = 0 ⇒Δ W = Δ U But, Δ U = nbsp;nC_V(T_2 T_1) ⇒Δ W = nC_V(T_1 T_2) We know that, hydrogen gas is a diatomic gas, ...

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Standard XIII

Physics

Thermodynamic Processes

In an adiabat...

Question

In an adiabatic process, $4 g$ of $H_{2}$ gas expands and temperature changes from $47^{\circ} C$ to $27^{\circ} C$ . Find the magnitude of the work done by the gas on the surrounding.

70 R

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80 R

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90 R

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100 R

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Solution

The correct option is D $100 R$
For an adiabatic process,
$Δ Q = Δ W + Δ U = 0$
$\Rightarrow Δ W = - Δ U$
But,
$Δ U = n C_{V} (T_{2} - T_{1})$
$\Rightarrow Δ W = n C_{V} (T_{1} - T_{2})$
We know that, hydrogen gas is a diatomic gas, so the number of degrees of freedom $(f) = 5$
Thus, specific heat capacity at constant volume $(C_{V}) = \frac{f R}{2} = \frac{5 R}{2}$
From the data given in the question,
$Δ W = 2 \times \frac{5}{2} R \times (47 - 27) = 100 R$
Hence, option (d) is the correct answer.

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Thermodynamic Processes

Standard XIII Physics

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In an adiabatic process, 4 g of H2 gas expands and temperature changes from 47∘C to 27∘C. Find the magnitude of the work done by the gas on the surrounding.

In an adiabatic process, $4 g$ of $H_{2}$ gas expands and temperature changes from $47^{\circ} C$ to $27^{\circ} C$ . Find the magnitude of the work done by the gas on the surrounding.