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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.900 K100 K915 K1.09 x 10 -3 K

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.900 K100 K915 K1.09 x 10 -3 K

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Solution

To find the final temperature of the gas, 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 gas constant, and T is the temperature.

First, let's convert the initial and final pressures from atmospheres to cm3. The initial pressure is 1 atmosphere, and the final pressure is 48 atmospheres.

Next, we need to find the initial and final volumes. The piston compresses 16 cm3 of fuel-air mixture into 1 cm3. Therefore, the initial volume is 16 cm3, and the final volume is 1 cm3.

Since the number of moles and the gas constant are constant, we can cancel them out in the equation.

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

T2 = (P2 * V1 * T1) / (P1 * V2)

Substituting the given values:

T2 = (48 * 16 * 305) / (1 * 1)

Calculating this expression, we find:

T2 = 232,320 / 1

Therefore, the final temperature is 232,320 K.

However, we need to consider the significant figures. The initial temperature is given as 305 K, which has three significant figures. Therefore, the final temperature should also have three significant figures.

Rounding the final temperature to three significant figures, we get:

T2 = 232,000 K

So, the final temperature of the gas is 232,000 K.

This problem has been solved

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