Answer :
we treat dry air as an ideal gas.
Volume = V1 T1 = 300 Kelvin Pressure = P1
V2 = V1 / 9 γ = ratio of specific heats = 1.5 T2 = ? P2 = ?
number of moles n is fixed.
P1 V1 / T1 = P2 V2 / T2
P1 V1 / 300 = P2 (V1 /9) / T2 => T2 = 33.33 P2 / P1
Is the gas compressed adiabatically and/or suddenly ? with no energy exchanged between the system and the environment ? It has to be mentioned whether it was an isobaric compression or adiabatic compression. Otherwise the final pressure is to be mentioned.
[tex]P V^{\gamma} = Constant\\V^{\gamma-1} T = constant\\V^{0.5}T=constant\\T=\frac{constant}{\sqrt{V}}\\\\\frac{T2}{T1}=\sqrt{\frac{V1}{V2}}[/tex]
T2 = 300 * √9 = 900⁰K = 627⁰ C
Volume = V1 T1 = 300 Kelvin Pressure = P1
V2 = V1 / 9 γ = ratio of specific heats = 1.5 T2 = ? P2 = ?
number of moles n is fixed.
P1 V1 / T1 = P2 V2 / T2
P1 V1 / 300 = P2 (V1 /9) / T2 => T2 = 33.33 P2 / P1
Is the gas compressed adiabatically and/or suddenly ? with no energy exchanged between the system and the environment ? It has to be mentioned whether it was an isobaric compression or adiabatic compression. Otherwise the final pressure is to be mentioned.
[tex]P V^{\gamma} = Constant\\V^{\gamma-1} T = constant\\V^{0.5}T=constant\\T=\frac{constant}{\sqrt{V}}\\\\\frac{T2}{T1}=\sqrt{\frac{V1}{V2}}[/tex]
T2 = 300 * √9 = 900⁰K = 627⁰ C
V₁ = V
V₂ = V/9
T₁ = 27⁰C = (27+273)K = 300K
T₂ = ?
[tex]T_1V_1^{\gamma -1}=T_2V_2^{\gamma -1}\\ \\ \Rightarrow T_2= \frac{T_1V_1^{\gamma -1}}{V_2^{\gamma -1}} \\ \\ \Rightarrow T_2=T_1( \frac{V_1}{V_2})^{\gamma -1}\\ \\ \Rightarrow T_2= 300 \times (\frac{V }{V/9})^{1.5-1}\\ \\ \Rightarrow T_2= 300 \times (9)^{0.5}\\ \\ \Rightarrow T_2= 300 \times 3=900K[/tex]
T₂ = 900K = 900-273 = 627°C
Answer is A.
V₂ = V/9
T₁ = 27⁰C = (27+273)K = 300K
T₂ = ?
[tex]T_1V_1^{\gamma -1}=T_2V_2^{\gamma -1}\\ \\ \Rightarrow T_2= \frac{T_1V_1^{\gamma -1}}{V_2^{\gamma -1}} \\ \\ \Rightarrow T_2=T_1( \frac{V_1}{V_2})^{\gamma -1}\\ \\ \Rightarrow T_2= 300 \times (\frac{V }{V/9})^{1.5-1}\\ \\ \Rightarrow T_2= 300 \times (9)^{0.5}\\ \\ \Rightarrow T_2= 300 \times 3=900K[/tex]
T₂ = 900K = 900-273 = 627°C
Answer is A.