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A diesel engine's piston compresses 16 cm3 of fuel-air mixture into 1 cm3. The pressure changes from 1 atmosphere to 48 atmospheres. If the initial temperature of the gas was 305 K, what was the final temperature?Note: As long as the units for pressure and volume are the same on both sides of the equation, they will cancel. Temperature, however, must be in units of kelvin. Be sure to use the proper number of significant figures.

Question

A diesel engine's piston compresses 16 cm3 of fuel-air mixture into 1 cm3. The pressure changes from 1 atmosphere to 48 atmospheres. If the initial temperature of the gas was 305 K, what was the final temperature?Note: As long as the units for pressure and volume are the same on both sides of the equation, they will cancel. Temperature, however, must be in units of kelvin. Be sure to use the proper number of significant figures.

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Solution

To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

First, let's convert the initial and final volumes to liters, as the ideal gas constant is typically given in liters.

Initial volume = 16 cm^3 = 16/1000 = 0.016 L Final volume = 1 cm^3 = 1/1000 = 0.001 L

Next, we need to find the initial and final pressures in atmospheres.

Initial pressure = 1 atmosphere Final pressure = 48 atmospheres

Now, we can rearrange the ideal gas law equation to solve for the final temperature:

T = (PV) / (nR)

Since the number of moles and the gas constant are constant, we can simplify the equation to:

T = (P1V1) / (P2V2)

Substituting the values:

T = (1 atm * 0.016 L) / (48 atm * 0.001 L) T = 0.016 / 0.048 T = 0.3333...

Finally, we need to convert the temperature from Celsius to Kelvin by adding 273.15:

T = 0.3333... + 273.15 T = 273.4833...

Therefore, the final temperature is approximately 273.48 K.

This problem has been solved

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