A gas with initial conditions p_i, V_i, and T_i expands isothermally until V_ f=6 V_i.
What are (a) T_f and (b) p_f? in terms of T_f/T_i and P_f/P_i
First I don't understand what this is saying at all. And Second I need to know how to solve it.
(a) If the gas expands isothermally, that means T is constant, so Tf = Ti
(b) When T = constant,
p*V = constant
Therefore
pi*Vi = pf*Vf = 6 pf*Vi
pf = pi/6
This problem describes an isothermal expansion of a gas from initial conditions to final conditions.
(a) To find T_f, we can use the ideal gas law:
P_i V_i / T_i = P_f V_f / T_f
Since it is an isothermal process, the initial and final temperatures are the same (T_i = T_f).
Therefore, we can simplify the equation to:
P_i V_i = P_f V_f
Substituting V_f = 6V_i, we have:
P_i V_i = P_f (6V_i)
Simplifying further:
P_f = P_i / 6
So, the final pressure (p_f) is 1/6 of the initial pressure (p_i).
(b) To find p_f, we use the same equation as above:
P_i V_i = P_f V_f
Substituting V_f = 6V_i, we have:
P_i V_i = P_f (6V_i)
Simplifying further:
P_f = P_i / 6
So, the final pressure (p_f) is 1/6 of the initial pressure (p_i).
In summary:
(a) T_f = T_i
(b) p_f = p_i / 6
Let's break down the problem and understand the given information:
We have a gas with initial conditions:
- Initial pressure (p_i)
- Initial volume (V_i)
- Initial temperature (T_i)
We are told that the gas expands isothermally, meaning its temperature remains constant during the expansion.
The gas expands until the final volume (V_f) is 6 times the initial volume (V_i). From this information, we can say V_f = 6V_i.
Now, let's solve for (a) T_f and (b) p_f in terms of T_f/T_i and P_f/P_i:
(a) To find T_f, we need to know the relationship between temperature and volume for an isothermal process. According to the ideal gas law, for an isothermal process, the pressure and volume are related by the equation:
P_i * V_i = P_f * V_f
Since V_f = 6V_i, we can substitute it into the equation:
P_i * V_i = P_f * 6V_i
Now, we can solve for the final pressure (P_f):
P_f = (P_i * V_i) / (6V_i)
P_f = P_i / 6
This means that the final pressure (P_f) is one-sixth of the initial pressure (P_i).
(b) Since the gas expands isothermally, the temperature stays constant. Therefore, T_f = T_i.
So, (a) T_f = T_i, and (b) P_f = P_i / 6, in terms of T_f/T_i and P_f/P_i.