Question 271: 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 cm
3
to 150 cm
3
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 cm 3 to 150 cm 3 adiabatically. In this process, the value of workdone on the gas will be :

Choose the correct answer: