Question 329: Thermodynamics & KTG

Question

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In this process, the value of workdone on the gas will be :

Accepted Answer

For monoatomic gas degree of freedom f = 3 and $$\gamma$$ = $${5 \over 3}$$
Here for gas,
Initial pressure (P
1
) = 75 kPa
Initial volume (V
1
) = 1200 cm
3
Final volume (V
2
) = 150 cm
3
Final pressure (P
2
) = ?
For adiabatic process,
$${P_1}V_1^\gamma  = {P_2}V_2^\gamma $$
$$ \Rightarrow 75 	imes {(1200)^\gamma } = {P_2}{(150)^\gamma }$$
$$ \Rightarrow {P_2} = 75 	imes {\left( {{{1200} \over {150}}} ight)^{{5 \over 3}}}$$
$$ = 75 	imes {(8)^{{5 \over 3}}}$$
$$ = 75 	imes 32$$ kPa
= 2400 kPa
Work done in adiabatic process,
$$W = {{{P_2}{V_2} - {P_1}{V_1}} \over {1 - \gamma }}$$
$$ = {{2400 	imes {{10}^3} 	imes 150 	imes {{10}^{ - 6}} - 75 	imes {{10}^3} 	imes 1200 	imes {{10}^{ - 6}}} \over {1 - {5 \over 3}}}$$
$$ = {{(2400 	imes 150 - 75 	imes 1200) 	imes {{10}^{ - 3}}} \over { - {2 \over 3}}}$$
$$ = {{ - 810000 	imes {{10}^{ - 3}}} \over 2}$$
$$ =  - 405$$ kJ

Answer

79 J

Answer

405 J

Answer

4050 J

Answer

9590 J

Thermodynamics & KTG

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In this process, the value of workdone on the gas will be :

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