Problem 2. Perfect Gas. In an automobile engine, a mixture of air and vaporized gasoline is compressed in the cylinders before being ignited. Typically, the volume of the mixture is compressed to 1/9th of its original volume (i.e., Vf = Vi/9) while the amount of gasoline (n) is kept constant. Assuming perfect gas law behavior, what is the final temperature of the compressed gas if the initial temperature is Ti = 27.0° C, the initial pressure is Pi = 1.00 atm, and the final pressure is Pf = 21.70 atm? Express your answer in both the Kelvin and Celsius temperature scales. (Note: the ratio 9.00 to 1.00 is called the compression ratio.). Remember, all calculations in thermodynamics are done in an absolute temperature scale, for example, Kelvin (K). Hint: Using the perfect gas law, solve for nR in terms of P, V, and T. Using this equation, write two equations—one for the initial uncompressed state and one for the final compressed state. Setting the two equations equal to each other, use the information given in the problem to solve for the final temperature (Tf ).
Problem 2. Perfect Gas. In an automobile engine, a mixture of air and vaporized gasoline is compressed in the cylinders before being ignited. Typically, the volume of the mixture is compressed to 1/9th of its original volume (i.e., Vf = Vi/9) while the amount of gasoline (n) is kept constant. Assuming perfect
(Note: the ratio 9.00 to 1.00 is called the compression ratio.). Remember, all calculations in
Hint: Using the perfect gas law, solve for nR in terms of P, V, and T. Using this equation, write two equations—one for the initial uncompressed state and one for the final compressed state. Setting the two equations equal to each other, use the information given in the problem to solve for the final temperature (Tf ).
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