Question

The cylinder in an automobile engine is heated, causing the piston to move and allowing the gas inside to expand at a constant pressure. The initial volume is 19.85 mL, and the initial temperature is 15.0 ºC. If the final volume is 25.5 mL, calculate the final temperature in degrees Celsius.

Answer 1

Using Charles's Law, we convert temperatures from Celsius to Kelvin, apply the formula V1/T1 = V2/T2, and solve for T2. After calculating, we find that the final temperature of the gas is 96.41 °C.

Step-by-step explanation:

To calculate the final temperature of a gas in a piston after expansion at constant pressure, we can use Charles's Law, which states that for a given mass of an ideal gas at constant pressure, the volume is directly proportional to the absolute temperature. The equation is V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.

We first need to convert the Celsius temperatures to Kelvin by adding 273.15, then we can solve for T2 as follows:

• Initial volume (V1) = 19.85 mL
• Initial temperature (T1) = 15.0 °C = 288.15 K
• Final volume (V2) = 25.5 mL

Using the formula:

(19.85 mL) / (288.15 K) = (25.5 mL) / T2

T2 = (25.5 mL * 288.15 K) / 19.85 mL

T2 = 369.56 K

Now convert the temperature back to Celsius:

T2 = 369.56 K - 273.15

T2 = 96.41 °C

The final temperature of the gas after the expansion is 96.41 °C.