To what temperature must a given mass of Nitrogen at zero degree celsius be heated to double its volume and pressure?

initial T = 0+273

P V= n R T
same n and R so
2P * 2V = n R (4T)
4*273 = 1092 K
which is
1092-273 = 819 C

T1=273 T2=546 V1=0 V2=0 Therefore V1 * T2=T1 * V2 V1 * 546=273 * V2 V1 divide by V2=273 divide by 546 answer is 0.5cm

p1v1=p2v2

P1=

To find the temperature at which a given mass of Nitrogen must be heated to double its volume and pressure, we need to use the ideal gas law.

The ideal gas law equation is given by:

PV = nRT

Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin

First, we need to convert the initial temperature of zero degrees Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature.

So, the initial temperature in Kelvin would be:

T1 = 0 + 273.15 = 273.15 K

Since the mass of Nitrogen is given, we can assume the number of moles of Nitrogen using its molar mass. The molar mass of Nitrogen is approximately 28 g/mol.

Next, assume the initial pressure and volume of Nitrogen to be P1 and V1, respectively.

Now, we have the initial conditions:
- Initial temperature (T1) = 273.15 K
- Initial pressure (P1)
- Initial volume (V1)

We want to find the final temperature (T2) at which the volume (V2) and pressure (P2) double.

Since we know that the volume is directly proportional to the temperature (T) and the pressure (P), we can express the relationship as:

(V2/V1) = (T2/T1) = (P2/P1)

We want to double the volume and pressure, so the ratios become:

(V2/V1) = 2
(P2/P1) = 2

Using this ratio equation, we can find the value of the final temperature (T2). Rearranging the equation, we get:

T2 = (V2/V1) * T1

Substituting the given values:

T2 = 2 * 273.15 K = 546.3 K

Finally, to convert the temperature back to Celsius, subtract 273.15 from the obtained value:

T2 = 546.3 - 273.15 ≈ 273.15 degrees Celsius

Therefore, to double the volume and pressure of a given mass of Nitrogen at zero degrees Celsius, it needs to be heated to approximately 273.15 degrees Celsius.