In an adiabatic compression of a gas with γ = 1.4, the final pressure

1.	In an adiabatic compression of a gas with γ = 1.4, the final pressure is double the initial pressure. If the initial temperature of the gas is 300 K, find the final temperature.
Answer» Data : \(\gamma\)= 1.4, P_f = 2P_i, T_i = 300K \(\frac{T_f}{T_i}\) = \((\frac{P_f}{P_i})^{(\gamma-1)/\gamma}\) = 2^{(1.4 - 1)/1.4} = 2^0.4/1.4 = 2^0.2857 ∴ log \(\frac{T_f}{T_i}\) = = 0.2857 log 2 = 0.2857 (0.3010) = 0.086 ∴ \(\frac{T_f}{T_i}\) = antilog 0.086 = 1.219 ∴ T_f = 1219T = (1.219) (300) = 365.7 K This is the final temperature of the gas.

In an adiabatic compression of a gas with γ = 1.4, the final pressure is double the initial pressure. If the initial temperature of the gas is 300 K, find the final temperature.

Answer»

Data : \(\gamma\)= 1.4, P_f = 2P_i, T_i = 300K

\(\frac{T_f}{T_i}\) = \((\frac{P_f}{P_i})^{(\gamma-1)/\gamma}\) = 2^{(1.4 - 1)/1.4} = 2^0.4/1.4 = 2^0.2857

∴ log \(\frac{T_f}{T_i}\) = = 0.2857 log 2 = 0.2857 (0.3010) = 0.086

∴ \(\frac{T_f}{T_i}\) = antilog 0.086 = 1.219

∴ T_f = 1219T

= (1.219) (300) = 365.7 K

This is the final temperature of the gas.

Discussion

No Comment Found

Related InterviewSolutions

`S_(H_(2(g)))^(0) = 130.6 J K^(-1) mol^(-1)`, `S_(H_(2)O_((l)))^(0)= 69.9 J K^(-1)mol^(-1)` `S_(O_(2(g)))^(0) = 205 J K^(-1)mol^(-1)`, then the absolute entropy change of `H_(2_((g))) + (1)/(2)O_(2_((g))) rarr H_(2)O_((l))` isA. `-163.2 J mol^(-1) K^(-1)`B. `+163.2 J mol^(-1)K^(-1)`C. `-303 J mol^(-1) K^(-1)`D. `+303 J mol^(-1) K^(-1)`
An intimate mixture of ferric oxide , `Fe_(2)O_(3)`, and aluminium, Al, is used in solid fuel rockets. Calculate the fuel value per gram and fuel value per cc. of the mixture . Heats of formation and densities are as follows `:-` `DeltaH_(f) (Al_(2)O_(3))= 399kcal//mol`, `DeltaH_(f)(Fe_(2)O_(3))= 199kcal//mol` Density of `Fe_(2)O_(3)= 5.2 g//cc`,Density of Al `= 2.7 g //cc.`
Calculate the entropy change for the conversion of2 moles of liquid water at 373K to vapours , if `Delta_(vap)` H is `37.3kJ mol^(-1)`.
Calculae the entropy change fo n-hexane when one mole of it evaporates at 341.7 K `(Delta_(vap) H = 29.0 kJ mol^(-1))`
An ideal gas has volume`V_(0)` at . `27^(@)C` It is heated at constant pressure so that its volume becomes . `2V_(0).`The final temperature isA. `54^(@)C`B. `32.6^(@)C`C. `327^(@)C`D. 150 k
What kind of system does a water filled bucket represents?
When a polyatomic gas undergoes an adiabatic process, its tempertaure and volume are related by the equation `TV^(n) =` constant, the value of `n`will beA. `1.33`B. `0.33`C. `2.33`D. `1`
A monoatomic gas undergoes adiabatic process. Its volume and temperature are related as `TV^(P)` = constant. The value of p will be `{:((1),1.33,(2),1.67),((3),0.67,(4),0.33):}`
For a given reaction `Delta`G obtained was having positive sign convention. State whether the reaction was spontaneous or non-spontaneous.
A gas is contained in a metallic cylinder fitted with a piston.The piston is suddenly moved in to compress the gas and is maintained at this position. As time passes the pressure of the gas in the cylinderA. The pressure decreasesB. The pressure increasesC. The pressure remains the sameD. The pressure may increase or decrease depending upon the nature of the gas

In an adiabatic compression of a gas with γ = 1.4, the final pressure is double the initial pressure. If the initial temperature of the gas is 300 K, find the final temperature.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment