Question

A student reduces the temperature from a 300 cm3 balloon from 60°C to 20°C. What will the new volume of the balloon be?

264 cm3

Answer 1

By applying Charles's law, the new volume of the balloon at 20°C is calculated to be 264 cm³ after converting the temperatures into Kelvin and using the direct proportionality between volume and temperature.

Step-by-step explanation:

The question involves the relationship between the volume and temperature of a gas at constant pressure, which is described by Charles's law. Charles's law states that the volume of an ideal gas is directly proportional to its temperature when the pressure is constant. To find the new volume of the balloon when the temperature is decreased from 60°C to 20°C, we first need to convert the temperatures from Celsius to Kelvin:

V1 = 300 cm3

T1 = 60°C = 333 K (60 + 273)

T2 = 20°C = 293 K (20 + 273)

Charles's law formula is V1/T1 = V2/T2. Let's calculate the new volume (V2).

V2 = (V1 × T2) / T1 V2 = (300 cm3 × 293 K) / 333 K V2 = 87900 cm3K / 333 K V2 = 264 cm3

Therefore, the new volume of the balloon at 20°C is 264 cm3.

Answer 2

To solve this we assume that the gas inside the balloon is an ideal gas. Then, we can use the ideal gas equation which is expressed as PV = nRT. At a constant pressure and number of moles of the gas the ratio T/V is equal to some constant. At another set of condition of temperature, the constant is still the same. Calculations are as follows:

T1 / V1 = T2 / V2

V2 = T2 x V1 / T1

V2 = 293.15 x 300 / 333.15

V2 = 263.98 cm^3