A diesel engine's piston compresses 16cm^3 of fuel-air mixture into 1cm^3 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. 915 K 1.09times 10^-3K 100 K 900 K

To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas before and after a change:<br /><br />\[<br />\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}<br />\]<br /><br />Where:<br />- \( P_1 = 1 \) atmosphere (initial pressure)<br />- \( V_1 = 16 \) cm³ (initial volume)<br />- \( T_1 = 305 \) K (initial temperature)<br />- \( P_2 = 48 \) atmospheres (final pressure)<br />- \( V_2 = 1 \) cm³ (final volume)<br />- \( T_2 \) is the final temperature we need to find.<br /><br />Rearranging the equation to solve for \( T_2 \):<br /><br />\[<br />T_2 = \frac{P_2 \times V_2 \times T_1}{P_1 \times V_1}<br />\]<br /><br />Substitute the known values into the equation:<br /><br />\[<br />T_2 = \frac{48 \times 1 \times 305}{1 \times 16}<br />\]<br /><br />Calculate \( T_2 \):<br /><br />\[<br />T_2 = \frac{14640}{16} = 915 \text{ K}<br />\]<br /><br />Therefore, the final temperature is 915 K.