Answer :
Final answer:
To determine the temperature of nitrogen gas at 175 kPa, use the combined gas law (P1/T1 = P2/T2). After converting the initial pressure from kPa to atm and applying the formula, the temperature is found to be 689.9 K.
Explanation:
To find the temperature of the nitrogen gas at 175 kPa, we can use the ideal gas law, which states that PV = nRT. However, as we are looking for the final temperature (T2) after a pressure change, and given that the number of moles (n) and the gas constant (R) do not change, we can use the combined gas law which comes from the ideal gas law: (P1V1/T1) = (P2V2/T2). Since the problem does not mention a change in volume, we assume it remains constant, and therefore, the V1 and V2 terms cancel out from the equation, leaving us with: (P1/T1) = (P2/T2).
To solve for T2: T2 = (P2 * T1) / P1.
First, convert 75.5 kPa to atm, because the ideal gas law typically uses atm for pressure (1 atm = 101.325 kPa).
P1 = 75.5 kPa * (1 atm/101.325 kPa) = 0.745 atm
T1 = 298 K (given)
P2 = 175 kPa * (1 atm/101.325 kPa) = 1.727 atm
T2 = (1.727 atm * 298 K) / 0.745 atm
Calculating this, T2 = 689.9 K.
The temperature of the nitrogen gas at 175 kPa is 689.9 K.
