30 cubic meters of argon gas are kept under constant pressure. The gas is heated from 10.0 degrees Celsius to 293 degrees Celsius. What is the new volume of the gas?

PV=kT is constant.

That means V/T = k/P is constant.
So, you want V such that

30/(273+10) = V/(273+293)

To find the new volume of the gas, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when the pressure remains constant.

Charles's Law can be expressed as:

V1/T1 = V2/T2

Where:
V1 = Initial volume of the gas
T1 = Initial temperature of the gas
V2 = Final volume of the gas (what we need to calculate)
T2 = Final temperature of the gas

Given:
V1 = 30 cubic meters
T1 = 10.0 degrees Celsius = 10.0 + 273.15 Kelvin (converting to Kelvin)
T2 = 293 degrees Celsius = 293 + 273.15 Kelvin (converting to Kelvin)

Now we can plug in the values into the formula:

30 / (10.0 + 273.15) = V2 / (293 + 273.15)

Simplifying the equation:

30 / 283.15 = V2 / 566.15

Cross-multiplying and solving for V2:

V2 = (30 / 283.15) * 566.15
≈ 60.06 cubic meters

Therefore, the new volume of the gas is approximately 60.06 cubic meters.