A certain volume of a gas at 298k is heated such that its volume and pressure are now four times their original value.what is the new temperature

see Steve's answer below.

298k

To find the new temperature, we can use the ideal gas law equation:

PV = nRT

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

Now, let's consider the initial state of the gas:

Initial pressure: P1
Initial volume: V1
Initial temperature: T1

And the final state of the gas:

Final pressure: P2 (four times the initial pressure)
Final volume: V2 (four times the initial volume)
Final temperature: T2 (the unknown variable we need to find)

Using the ideal gas law, we can rewrite the equation for the initial state as:

P1V1 = nRT1

And the equation for the final state as:

P2V2 = nRT2

Since the number of moles (n) and the gas constant (R) are constant, we can rearrange the equations to solve for the unknown temperature (T2):

T2 = (P2V2 * T1) / (P1V1)

Given that the initial volume and pressure are quadrupled, we have:

P2 = 4 * P1
V2 = 4 * V1

Substituting these values into the equation, we get:

T2 = (4 * P1 * 4 * V1 * T1) / (P1 * V1)

Simplifying further:

T2 = 16 * T1

Therefore, the new temperature (T2) will be 16 times the initial temperature (T1).