A monatomic ideal gas expands from 1.00m^3 to 2.50m^3 st a constant pressure of 2.00x10^5 Pa. Find the change in the internal energy of the gas.
Internal energy is U=3•n•R•T/2 => chage in internal energy is ΔU=3•n•R•ΔT/2.
From the ideal gas law PV=nRT =>
n•R•ΔT=nR(T2-T1)=p2•V2 =p1•V1=p(V2-V1) =>
ΔU=3•n•R•ΔT/2=3•p(V2-V1)/2=3•2•10⁵•(2.5-1)/2=4.5•10⁵ J
Well, when it comes to gases expanding, I like to think of it as the gas getting a little more room to stretch its, um, molecular legs. Now, the internal energy of a monatomic ideal gas depends solely on its temperature, so we can forget about any shenanigans with changing temperatures in this case.
To find the change in internal energy, we can use the formula:
ΔU = PΔV
where ΔU is the change in internal energy, P is the pressure, and ΔV is the change in volume.
In this case, the pressure is given as 2.00x10^5 Pa, and the change in volume is (2.50m^3 - 1.00m^3) = 1.50m^3.
So, plugging in the values into the formula, we have:
ΔU = (2.00x10^5 Pa) * (1.50m^3)
= 3.00x10^5 J
Therefore, the change in the internal energy of the gas is 3.00x10^5 Joules.
I hope that answers your question without too many gasps for air!
To find the change in internal energy of the gas, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added (Q) to the system minus the work done (W) by the system:
ΔU = Q - W
Given that the gas expands at a constant pressure, the work done by the gas can be calculated using the formula:
W = PΔV
where P is the pressure and ΔV is the change in volume.
In this case, the gas expands from an initial volume of 1.00 m^3 to a final volume of 2.50 m^3, so ΔV = 2.50 m^3 - 1.00 m^3 = 1.50 m^3.
The pressure of the gas is given as 2.00 × 10^5 Pa.
Using the formula for work, we can calculate the work done by the gas:
W = (2.00 × 10^5 Pa) × (1.50 m^3) = 3.00 × 10^5 J
To find the change in internal energy, we need to know if any heat is added to or removed from the system. However, the problem does not provide information about the heat transfer.
If we assume that there is no heat transfer (Q = 0), then we can find the change in internal energy:
ΔU = Q - W = 0 - (3.00 × 10^5 J) = -3.00 × 10^5 J
Therefore, the change in internal energy of the gas is -3.00 × 10^5 J.
To find the change in internal energy of the gas, we need to use the equation:
ΔU = Q - W
Where ΔU represents the change in internal energy, Q represents the heat transferred to the gas, and W represents the work done by (or on) the gas.
In this case, the process is happening at a constant pressure, so we can use the equation for work done by a gas at constant pressure:
W = PΔV
Where P is the pressure of the gas and ΔV is the change in volume.
Now let's calculate the values:
Given:
P = 2.00x10^5 Pa
ΔV = 2.50m^3 - 1.00m^3 = 1.50m^3
First, let's calculate the work done:
W = PΔV
W = (2.00x10^5 Pa)(1.50m^3)
W = 3.00x10^5 J
Next, let's calculate the change in internal energy. Since the process is happening at constant pressure, there is no heat transfer (Q = 0).
ΔU = Q - W
ΔU = 0 - 3.00x10^5 J
ΔU = -3.00x10^5 J
Therefore, the change in internal energy of the gas is -3.00x10^5 J.