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  • A liter of dry air at STP expands adiabatically to a volume of 3l. If , then work done (in J ) by air is <img alt="(3^{1.4}=4.6555)" src="http:

A liter of dry air at STP expands adiabatically to a volume of 3l. If \gamma=1.40, then work done (in J ) by air is (3^{1.4}=4.6555) [take air to be an ideal gas]:-  
 
Option: 1 90.5
Option: 2 100.8
Option: 3 60.7  
Option: 4 48
 

Answers (1)

best_answer

 

 

Adiabatic process -

Work done in adiabatic process - 

                                    W=\int_{V_{i}}^{V_{f}} P d V=\int_{V_{i}}^{V_{f}} \frac{K}{V^{\gamma}} d V \Rightarrow W=\frac{\left[P_{i} V_{i}-P_{f} V_{f}\right]}{(\gamma-1)}=\frac{\mu R\left(T_{i}-T_{f}\right)}{(\gamma-1)}

 

    

W_{adiabatic} = \frac{P_1V_1 - P_2V_2}{\gamma -1}

At STP, Pressure = P1 = 100000 Pascal

             Volume = V1 = 1 liter (As given in question)

So,

 \\ P_1V^{\gamma}_1 = P_2V^{\gamma}_2 \\ \\ \Rightarrow \ 1 \times (1)^{\gamma} = P_2 \times (3)^{1.4} \\ \\ P_2 = \frac{1}{4.65}\ atm \\

W_{adiabatic} = (\frac{1\ \times {1} - \frac{1}{4.65} \times {3}}{0.4}) \times 101.33 \\ \\ = 90.5 \ Joule

 

So, option (3) is correct.

Posted by

Ritika Jonwal

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