a) If the pressure and volume of a gas both increase, will the temperature increase or decrease?
b) If the pressure is doubled and the volume is tripled, by what factor must the temperature increase or decrease?
c) If the pressure of the gas is decreased by removing some of the gas, is it possible to use the above formula to predict the change in volume and temperature? Why or why not?
c) If the pressure of the gas is decreased by removing some of the gas, is it possible to use the above formula to predict the change in volume and temperature? Why or why not?
a) PV = nRT
If the left side increases, what must the right side do? Since n and R and constant, what does that mean about T>
b) If P is doubled and V is tripled, the left side increases by a factor of 6 so the right side must ????????? by a factor of 6, too?
c) If you know how much gas was there initially and how much was removed, yes, but if no knowledge of n is available, no. Besides predicting BOTH V and T mean two unknowns.
a) According to the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature. If both pressure and volume increase, the value of PV increases. Since the value of n and R remain constant, and the value of PV increases, the temperature (T) must also increase to compensate and maintain the equality of the equation.
b) If the pressure is doubled and the volume is tripled, we can use the ideal gas law to determine the change in temperature. The formula for the ideal gas law can be rearranged as T = PV/(nR).
Let's assume the initial temperature is T1, and after doubling the pressure (2P) and tripling the volume (3V), the temperature becomes T2.
Using the ideal gas law, we can set up the following equation:
T1 = P * V / (n * R)
T2 = (2P) * (3V) / (n * R)
To find the factor by which the temperature changes, we divide the second equation by the first:
T2/T1 = [(2P)*(3V)/(n*R)] / [(P*V)/(n*R)]
Simplifying the equation:
T2/T1 = [(2P)*(3V)] / [(P*V)]
T2/T1 = 6
Therefore, the temperature must increase by a factor of 6.
c) If the pressure of the gas is decreased by removing some of the gas, it is still possible to use the ideal gas law to predict the change in volume and temperature. However, without additional information about the system, such as the initial and final pressure values, it would be difficult to determine the exact changes in volume and temperature. The ideal gas law can provide a relationship between pressure, volume, and temperature, but the specific changes would require more information.