To determine the increase in temperature when the pressure is increased from 30 Pa to 90 Pa, we need to use the ideal gas law. The ideal gas law states that for an ideal gas, the pressure (P), volume (V), and temperature (T) are related by the equation:
PV = nRT
Where: P = Pressure V = Volume n = Number of moles of gas R = Ideal gas constant T = Temperature in Kelvin
Assuming the volume and the number of moles of gas remain constant, we can rewrite the ideal gas law equation as:
P/T = constant
From this equation, we can see that pressure (P) and temperature (T) are directly proportional when volume and the number of moles are constant.
Let's calculate the increase in temperature:
Initial pressure (P1) = 30 Pa Final pressure (P2) = 90 Pa
Using the ratio of pressures and temperatures:
P1/T1 = P2/T2
Rearranging the equation to solve for the change in temperature (ΔT):
ΔT = T2 - T1 = T1 * (P2/P1 - 1)
Converting pressures to Kelvin by using absolute temperature:
T1 = 273 K (assumed initial temperature at 0 degrees Celsius) T2 = T1 * (P2/P1 - 1)
Substituting the values:
T2 = 273 K * (90 Pa / 30 Pa - 1)
Calculating:
T2 = 273 K * (3 - 1) = 546 K
Therefore, the increase in temperature when the pressure is increased from 30 Pa to 90 Pa is 546 K - 273 K = 273 K.