10 mol of an ideal gas expands isothermally at 373 K to 2.6 times its initial volume. Find the heat flow into the system. The universal gas constant is 8.31 J/K · mol.
Answer in units of J.
Any help much appreciated, I have no idea where to begin with this problem.
To solve this problem, we can use the ideal gas law and the first law of thermodynamics.
The ideal gas law states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = universal gas constant
T = temperature of the gas
In this problem, we are given:
n = 10 mol (moles)
V2 = 2.6V1 (final volume is 2.6 times larger than the initial volume)
T = 373 K (isothermal process)
R = 8.31 J/(K·mol)
To find the heat flow into the system, we need to calculate the work done by the system and use the first law of thermodynamics.
The first law of thermodynamics states:
ΔU = Q - W
Where:
ΔU = change in internal energy of the system
Q = heat flow into the system
W = work done by the system
Since the process is isothermal, ΔU = 0 (there is no change in internal energy).
Therefore, Q = W
To calculate the work done by the system, we can use the equation:
W = -PΔV
Since the gas expands, ΔV is positive. Therefore, the work done by the system is negative.
Rearranging the ideal gas law equation to solve for P, we get:
P = (nRT) / V
Substituting the given values:
P1 = (10 mol)(8.31 J/(K·mol))(373 K) / V1
P2 = (10 mol)(8.31 J/(K·mol))(373 K) / V2
Substituting these pressure values into the work equation, we get:
W = -P1(2.6V1 - V1)
W = -P1(1.6V1)
Now we can calculate the work done. But remember, the work done is equal to the heat flow into the system, so Q = W.
Using the given values, plug them into the equation to get the answer in units of J.
I hope this explanation helps you understand how to approach this problem!