Final answer:
By applying Charles's Law and assuming constant pressure, we calculate the unknown outside temperature to be approximately -60.96°C when the gas in the piston has a volume of 5 L, given that at 1000°C the volume is 30 L.
Step-by-step explanation:
The student's question is concerning the relationship between the volume of a gas in a piston at a known temperature and the volume of the gas at an unknown temperature. This is a physics problem involving the principles of thermodynamics, specifically Charles's Law (or Gay-Lussac's Law) which states that for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its temperature in kelvins.
To solve for the unknown temperature, we assume the pressure and the amount of gas remain constant, and the temperature scale is in Kelvin. The formula is:
V1 / T1 = V2 / T2
Where:
V1 is the initial volume
T1 is the initial temperature in Kelvin
V2 is the final volume
T2 is the final temperature in Kelvin
To find the temperature outside (T2) when the volume of the piston is 5 liters (V2) and knowing that at 1000°C (T1) the volume (V1) is 30 liters, we first convert the temperature from Celsius to Kelvin by adding 273.15, which gives us 1273.15 K. Now we use the formula:
T2 = V2 × T1 / V1
T2 = 5 L × 1273.15 K / 30 L
T2 = 212.1925 K
Converting back to Celsius:
T2°C = 212.1925 K - 273.15
T2°C = -60.9575°C
Therefore, the outside temperature is approximately -60.96°C.