Question 969: Thermodynamics & KTG

Question

A mass of diatomic gas $$(\gamma  = 1.4)$$ at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27
o
C to 927
o
C. The pressure of the gas in the final state is

Accepted Answer

T
1
= 273 + 27 = 300K
T
2
= 273 + 927 = 1200K
For adiabatic process,
$${P^{1 - \gamma }}{T^\gamma }$$ = constant
$$ \Rightarrow {P_1}^{1 - \gamma }{T_1}^\gamma  = {P_2}^{1 - \gamma }{T_2}^\gamma $$
$$ \Rightarrow {\left( {{{{P_2}} \over {{P_1}}}} \right)^{1 - \gamma }} = {\left( {{{{T_1}} \over {{T_2}}}} \right)^\gamma }$$
$$ \Rightarrow {\left( {{{{P_1}} \over {{T_2}}}} \right)^{1 - \gamma }} = {\left( {{{{T_2}} \over {{T_1}}}} \right)^\gamma }$$
$${\left( {{{{P_1}} \over {{P_2}}}} \right)^{1 - 1.4}} = {\left( {{{1200} \over {300}}} \right)^{1.4}}$$
$${\left( {{{{P_1}} \over {{P_2}}}} \right)^{ - 0.4}} = {\left( 4 \right)^{1.4}}$$
$${\left( {{{{P_2}} \over {{P_1}}}} \right)^{0.4}} = {4^{1.4}}$$
$${P_2} = {P_1}{4^{\left( {{{1.4} \over {0.4}}} \right)}} = {P_1}{4^{\left( {{7 \over 2}} \right)}}$$
= P
1
(2
7
) = 2 ÃÂ 128 = 256 atm

Answer

8 atm

Answer

28 atm

Answer

68.7 atm

Answer

256 atm

Thermodynamics & KTG

A mass of diatomic gas $(\gamma = 1.4)$ at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27 o C to 927 o C. The pressure of the gas in the final state is

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