P V/T = n R
n and R are the same for both
P1 V1/T1 = P2 V2/T2
P1 V1 T2 = P2 V2 T1
T2 = T1 (P2/P1)(V2/V1)
luckily using degrees Kelvin so
T2 = 300 (3.5/2)(12/15)
n and R are the same for both
P1 V1/T1 = P2 V2/T2
P1 V1 T2 = P2 V2 T1
T2 = T1 (P2/P1)(V2/V1)
luckily using degrees Kelvin so
T2 = 300 (3.5/2)(12/15)
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
In this case, we have the initial conditions represented by subscripts "i" and the final conditions represented by subscripts "f":
P_i = 2·10^5 Pa
V_i = 15 dm^3
T_i = 300 K
P_f = 3.5·10^5 Pa
V_f = 12 dm^3
T_f = ? (what we want to find)
Since the number of moles is constant, it cancels out in the equation. So we can rewrite the equation as:
P_i * V_i / T_i = P_f * V_f / T_f
Now we can rearrange the equation to solve for T_f:
T_f = (P_f * V_f * T_i) / (P_i * V_i)
Substituting the given values:
T_f = (3.5·10^5 Pa * 12 dm^3 * 300 K) / (2·10^5 Pa * 15 dm^3)
Now we can calculate the final temperature:
T_f = 2520 K
Therefore, the final temperature of the gas is 2520 K.