We can use the ideal gas law to solve this problem:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Assuming that the number of moles of gas and the pressure are constant, we can write:
V/T = constant
This means that the product of volume and temperature is constant as long as the pressure and the number of moles of gas are held constant.
We can use this relationship to solve the problem.
Let V1 be the initial volume of the gas (150 cm³) and T1 be the initial temperature in Kelvin. Let V2 be the final volume of the gas (250 cm³) and T2 be the final temperature in Kelvin.
We can write:
V1/T1 = V2/T2
Solving for T2:
T2 = (V2/V1) * T1
The cubic expansitivity of gas at constant pressure is given by:
1/273K-1
We can convert the initial temperature from Celsius to Kelvin:
T1 = (0°C + 273.15) K = 273.15 K
Plugging in the values, we get:
T2 = (250 cm³ / 150 cm³) * 273.15 K
T2 = 455.25 K
Therefore, the temperature of the gas when its volume is 250 cm³ is 455.25 K (182.1°C).