To what Celsius temperature must a gas sample initially at 20 degrees Celsius be heated if its volume is to double while the pressure remains the same?

P1V1/T1=P2V2/T2

V2/V1=T2/T1 if P1=P2

T1=273+20=293
therefore, T2= 2*293K
T2= 293C

293C

To find the temperature at which the gas sample needs to be heated in order for its volume to double while the pressure remains the same, we can use the relationship known as Charles's Law.

Charles's Law states that for a given amount of gas at a constant pressure, the volume is directly proportional to the temperature in Kelvin.

We can use the following formula to solve the problem:

V₁ / T₁ = V₂ / T₂

Where:
V₁ = initial volume
T₁ = initial temperature (in Kelvin)
V₂ = final volume (twice the initial volume)
T₂ = final temperature (what we're trying to find)

Let's start by converting the temperatures from Celsius to Kelvin. The Kelvin temperature scale does not use negative values, therefore we need to add 273.15 to the Celsius temperature.

T₁ = 20°C + 273.15 = 293.15 K (initial temperature)
V₁ = initial volume
V₂ = 2 × V₁ (final volume)

Now we can set up the equation:

V₁ / 293.15 = (2 × V₁) / T₂

Next, we can simplify the equation by cross-multiplying:

V₁ × T₂ = (2 × V₁) × 293.15

We can further simplify the equation:

T₂ = (2 × V₁ × 293.15) / V₁

The V₁ terms on both sides of the equation cancel out, leaving us with:

T₂ = 2 × 293.15

Finally, we can solve for T₂:

T₂ = 586.30 K

To convert this temperature back to Celsius, we subtract 273.15:

T₂ = 586.30 K - 273.15 = 313.15°C

Therefore, the gas sample must be heated to 313.15 degrees Celsius in order for its volume to double while the pressure remains the same.